{"id":4446,"date":"2020-04-13T13:33:33","date_gmt":"2020-04-13T13:33:33","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=4446"},"modified":"2021-02-06T00:04:31","modified_gmt":"2021-02-06T00:04:31","slug":"using-the-properties-of-rectangles-to-solve-problems","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/using-the-properties-of-rectangles-to-solve-problems\/","title":{"raw":"Using the Properties of Rectangles to Solve Problems","rendered":"Using the Properties of Rectangles to Solve Problems"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Find perimeter and area of a rectangle given length and width<\/li>\r\n \t<li>Find dimensions of a rectangle given perimeter and a relationship between length and width<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p>A rectangle has four sides and four right angles. The opposite sides of a rectangle are the same length. We refer to one side of the rectangle as the length, [latex]L[\/latex], and the adjacent side as the width, [latex]W[\/latex]. See the image below.<\/p>\r\nA rectangle has four sides, and four right angles. The sides are labeled L for length and W for width.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223837\/CNX_BMath_Figure_09_04_012.png\" alt=\"A rectangle is shown. Each angle is marked with a square. The top and bottom are labeled [latex]L[\/latex], the sides are labeled [latex]W[\/latex].\" \/>\r\nThe perimeter, [latex]P[\/latex], of the rectangle is the distance around the rectangle. If you started at one corner and walked around the rectangle, you would walk [latex]L+W+L+W[\/latex] units, or two lengths and two widths. The perimeter then is\r\n<p style=\"text-align: center\">[latex]\\begin{array}{c}P=L+W+L+W\\hfill \\\\ \\hfill \\text{or}\\hfill \\\\ P=2L+2W\\hfill \\end{array}[\/latex]<\/p>\r\nWhat about the area of a rectangle? Remember the rectangular rug from the beginning of this section. It was [latex]2[\/latex] feet long by [latex]3[\/latex] feet wide, and its area was [latex]6[\/latex] square feet. See the image below. Since [latex]A=2\\cdot 3[\/latex], we see that the area, [latex]A[\/latex], is the length, [latex]L[\/latex], times the width, [latex]W[\/latex], so the area of a rectangle is [latex]A=L\\cdot W[\/latex].\r\n\r\nThe area of this rectangular rug is [latex]6[\/latex] square feet, its length times its width.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223838\/CNX_BMath_Figure_09_04_013.png\" alt=\"A rectangle is shown. It is made up of 6 squares. The bottom is 2 squares across and marked as 2, the side is 3 squares long and marked as 3.\" \/>\r\n<div class=\"textbox shaded\">\r\n<h3>Properties of Rectangles<\/h3>\r\n<ul id=\"fs-id1171497076758\">\r\n \t<li>Rectangles have four sides and four right [latex]\\left(\\text{90}^ \\circ\\right)[\/latex] angles.<\/li>\r\n \t<li>The lengths of opposite sides are equal.<\/li>\r\n \t<li>The perimeter, [latex]P[\/latex], of a rectangle is the sum of twice the length and twice the width. See the first image. [latex]P=2L+2W[\/latex]<\/li>\r\n \t<li>The area, [latex]A[\/latex], of a rectangle is the length times the width. [latex]A=L\\cdot W[\/latex]<\/li>\r\n<\/ul>\r\n<\/div>\r\nFor easy reference as we work the examples in this section, we will restate the Problem Solving Strategy for Geometry Applications here.\r\n<div class=\"textbox shaded\">\r\n<h3>Use a Problem Solving Strategy for Geometry Applications<\/h3>\r\n<ol id=\"eip-id1170325029073\" class=\"stepwise\">\r\n \t<li><strong>Read<\/strong> the problem and make sure you understand all the words and ideas. Draw the figure and label it with the given information.<\/li>\r\n \t<li><strong>Identify<\/strong> what you are looking for.<\/li>\r\n \t<li><strong>Name<\/strong> what you are looking for. Choose a variable to represent that quantity.<\/li>\r\n \t<li><strong>Translate<\/strong> into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.<\/li>\r\n \t<li><strong>Solve<\/strong> the equation using good algebra techniques.<\/li>\r\n \t<li><strong>Check<\/strong> the answer in the problem and make sure it makes sense.<\/li>\r\n \t<li><strong>Answer<\/strong> the question with a complete sentence.<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThe length of a rectangle is [latex]32[\/latex] meters and the width is [latex]20[\/latex] meters.\r\n\r\n1. Find the perimeter\r\n\r\n2. Find the area\r\n\r\nSolution\r\n<table id=\"eip-id1168468455627\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223840\/CNX_BMath_Figure_09_04_067_img_MW-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td>the perimeter of a rectangle<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>Let [latex]P[\/latex] = the perimeter<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong>Translate.<\/strong>\r\n\r\nWrite the appropriate formula.\r\n\r\nSubstitute.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223841\/CNX_BMath_Figure_09_04_067_img_MW-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td>[latex]P=64+40[\/latex]\r\n\r\n[latex]P=104[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong>\r\n\r\n[latex]p\\stackrel{?}{=}104[\/latex]\r\n\r\n[latex]20+32+20+32\\stackrel{?}{=}104[\/latex]\r\n\r\n[latex]104=104\\checkmark[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\r\n<td>The perimeter of the rectangle is [latex]104[\/latex] meters.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168467114806\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223845\/CNX_BMath_Figure_09_04_068_img_MW-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td>the area of a rectangle<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>Let <em>A<\/em> = the area<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong>Translate.<\/strong>\r\n\r\nWrite the appropriate formula.\r\n\r\nSubstitute.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223846\/CNX_BMath_Figure_09_04_068_img_MW-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td>[latex]A=640[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong>\r\n\r\n[latex]A\\stackrel{?}{=}640[\/latex]\r\n\r\n[latex]32\\cdot 20\\stackrel{?}{=}640[\/latex]\r\n\r\n[latex]640=640\\checkmark[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\r\n<td>The area of the rectangle is [latex]640[\/latex] square meters.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146510[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nFind the length of a rectangle with perimeter [latex]50[\/latex] inches and width [latex]10[\/latex] inches.\r\n[reveal-answer q=\"172562\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"172562\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168469470101\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \">\r\n<tbody>\r\n<tr>\r\n<td>Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223850\/CNX_BMath_Figure_09_04_069_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td>the length of the rectangle<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>Let\u00a0[latex]L[\/latex] = the length<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong>Translate.<\/strong>\r\n\r\nWrite the appropriate formula.\r\n\r\nSubstitute.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223852\/CNX_BMath_Figure_09_04_069_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td>[latex]50\\color{red}{- 20}=2L+20\\color{red}{- 20}[\/latex]\r\n\r\n[latex]30=2L[\/latex]\r\n\r\n[latex]{\\Large\\frac{30}{\\color{red}{2}}}={\\Large\\frac{2L}{\\color{red}{2}}}[\/latex]\r\n\r\n[latex]15=L[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong>\r\n\r\n[latex]p=50[\/latex]\r\n\r\n[latex]15+10+15+10\\stackrel{?}{=}50[\/latex]\r\n\r\n[latex]50=50\\checkmark[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\r\n<td>The length is [latex]15[\/latex] inches.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146518[\/ohm_question]\r\n\r\n<\/div>\r\nIn the next example, the width is defined in terms of the length. We\u2019ll wait to draw the figure until we write an expression for the width so that we can label one side with that expression.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThe width of a rectangle is two inches less than the length. The perimeter is [latex]52[\/latex] inches. Find the length and width.\r\n[reveal-answer q=\"886120\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"886120\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168466427903\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \" width=\"\">\r\n<tbody>\r\n<tr>\r\n<td>Step 1. <strong>Read<\/strong> the problem.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td>the length and width of the rectangle<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.\r\n\r\nNow we can draw a figure using these expressions for the length and width.<\/td>\r\n<td>Since the width is defined in terms of the length, we let <em>L<\/em> = length. The width is two feet less that the length, so we let <em>L<\/em> \u2212 2 = width\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223855\/CNX_BMath_Figure_09_04_070_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4.<strong>Translate.<\/strong>\r\n\r\nWrite the appropriate formula. The formula for the perimeter of a rectangle relates all the information.\r\n\r\nSubstitute in the given information.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223856\/CNX_BMath_Figure_09_04_070_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td>[latex]52=2L+2L - 4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>[latex]52=4L - 4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add [latex]4[\/latex] to each side.<\/td>\r\n<td>[latex]56=4L[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide by [latex]4[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{56}{4}}={\\Large\\frac{4L}{4}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]14=L[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>The length is [latex]14[\/latex] inches.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Now we need to find the width.<\/td>\r\n<td>\u00a0[latex]L-2[\/latex]\r\n\r\n[latex]\\color{red}{14}-2[\/latex]\r\n\r\n[latex]12[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The width is [latex]L\u22122[\/latex].<\/td>\r\n<td>&nbsp;\r\n\r\nThe width is [latex]12[\/latex] inches.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong>\r\n\r\nSince [latex]14+12+14+12=52[\/latex] , this works!<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\r\n<td>The length is [latex]14[\/latex] feet and the width is [latex]12[\/latex] feet.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146504[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThe length of a rectangle is four centimeters more than twice the width. The perimeter is [latex]32[\/latex] centimeters. Find the length and width.\r\n[reveal-answer q=\"869311\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"869311\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468670350\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \" width=\"\">\r\n<tbody>\r\n<tr>\r\n<td>Step 1. <strong>Read<\/strong> the problem.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td>the length and width<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>let <em>W<\/em> = width\r\n\r\nThe length is four more than twice the width.\r\n\r\n[latex]2w+4[\/latex] = length\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223858\/CNX_BMath_Figure_09_04_071_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4.<strong>Translate.<\/strong>\r\n\r\nWrite the appropriate formula and substitute in the given information.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223900\/CNX_BMath_Figure_09_04_071_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td>[latex]32=4w+8+2w[\/latex]\r\n\r\n[latex]32=6w+8[\/latex]\r\n\r\n[latex]24=6w[\/latex]\r\n\r\n[latex]4=w[\/latex] (width)\r\n\r\n[latex]2w+4=[\/latex] length\r\n\r\n[latex]2(\\color{red}{4})+4[\/latex]\r\n\r\n[latex]8+4=12[\/latex]\r\n\r\nThe length is\u00a0[latex]12[\/latex]cm.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong>\r\n\r\n[latex]P=2L+2W[\/latex]\r\n\r\n[latex]P\\stackrel{?}{=}2\\cdot 12+2\\cdot 4[\/latex]\r\n\r\n[latex]32=32\\quad\\checkmark[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\r\n<td>The length is [latex]12[\/latex] cm and the width is [latex]4[\/latex] cm.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146521[\/ohm_question]\r\n\r\n[ohm_question]146522[\/ohm_question]\r\n\r\n<\/div>\r\nWatch this video to see another similar example of finding area given the relationship between the length and width of a rectangle.\r\n\r\nhttps:\/\/youtu.be\/zUlU64Umnq4\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThe area of a rectangular room is [latex]168[\/latex] square feet. The length is [latex]14[\/latex] feet. What is the width?\r\n[reveal-answer q=\"247910\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"247910\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168466072798\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \" width=\"\">\r\n<tbody>\r\n<tr>\r\n<td>Step 1. <strong>Read<\/strong> the problem.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223903\/CNX_BMath_Figure_09_04_083_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td>the width of a rectangular room<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\r\n<td>Let <em>W<\/em> = width<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4.<strong>Translate.<\/strong>\r\n\r\nWrite the appropriate formula and substitute in the given information.<\/td>\r\n<td>[latex]A=LW[\/latex]\r\n\r\n[latex]168=14W[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td>[latex]\\Large\\frac{168}{14}\\normalsize=\r\n\r\n\\Large\\frac{14W}{14}[\/latex]\r\n\r\n[latex]12=W[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong>\r\n\r\n[latex]A=LW[\/latex]\r\n\r\n[latex]168\\stackrel{?}{=}14\\cdot 12[\/latex]\r\n\r\n[latex]168=168\\checkmark[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\r\n<td>The width of the room is [latex]12[\/latex] feet.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146523[\/ohm_question]\r\n\r\n<\/div>\r\nIn the next example you will see a similar application involving perimeter, length, and width.\r\n\r\nhttps:\/\/youtu.be\/jlxPgKQfhQs\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThe perimeter of a rectangular swimming pool is [latex]150[\/latex] feet. The length is [latex]15[\/latex] feet more than the width. Find the length and width.\r\n[reveal-answer q=\"207235\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"207235\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168469520954\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \" width=\"\">\r\n<tbody>\r\n<tr>\r\n<td>Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223907\/CNX_BMath_Figure_09_04_072.img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td>the length and width of the pool<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.\r\n\r\nThe length is [latex]15[\/latex] feet more than the width.<\/td>\r\n<td>Let [latex]W=\\text{width}[\/latex]\r\n\r\n[latex]W+15=\\text{length}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4.<strong>Translate.<\/strong>\r\n\r\nWrite the appropriate formula and substitute.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223908\/CNX_BMath_Figure_09_04_072_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td>[latex]150=2w+30+2w[\/latex]\r\n\r\n[latex]150=4w+30[\/latex]\r\n\r\n[latex]120=4w[\/latex]\r\n\r\n[latex]30=w[\/latex] the width of the pool.\r\n\r\n[latex]w+15[\/latex] the length of the pool.\r\n\r\n[latex]\\color{red}{30}+15[\/latex]\r\n\r\n[latex]45[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong>\r\n\r\n[latex]P=2L+2W[\/latex]\r\n\r\n[latex]150\\stackrel{?}{=}2(45)+2(30)[\/latex]\r\n\r\n[latex]150=150\\checkmark[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\r\n<td>The length of the pool is [latex]45[\/latex] feet and the width is [latex]30[\/latex] feet.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146524[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Find perimeter and area of a rectangle given length and width<\/li>\n<li>Find dimensions of a rectangle given perimeter and a relationship between length and width<\/li>\n<\/ul>\n<\/div>\n<p>A rectangle has four sides and four right angles. The opposite sides of a rectangle are the same length. We refer to one side of the rectangle as the length, [latex]L[\/latex], and the adjacent side as the width, [latex]W[\/latex]. See the image below.<\/p>\n<p>A rectangle has four sides, and four right angles. The sides are labeled L for length and W for width.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223837\/CNX_BMath_Figure_09_04_012.png\" alt=\"A rectangle is shown. Each angle is marked with a square. The top and bottom are labeled [latex]L[\/latex], the sides are labeled [latex]W[\/latex].\" \/><br \/>\nThe perimeter, [latex]P[\/latex], of the rectangle is the distance around the rectangle. If you started at one corner and walked around the rectangle, you would walk [latex]L+W+L+W[\/latex] units, or two lengths and two widths. The perimeter then is<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{c}P=L+W+L+W\\hfill \\\\ \\hfill \\text{or}\\hfill \\\\ P=2L+2W\\hfill \\end{array}[\/latex]<\/p>\n<p>What about the area of a rectangle? Remember the rectangular rug from the beginning of this section. It was [latex]2[\/latex] feet long by [latex]3[\/latex] feet wide, and its area was [latex]6[\/latex] square feet. See the image below. Since [latex]A=2\\cdot 3[\/latex], we see that the area, [latex]A[\/latex], is the length, [latex]L[\/latex], times the width, [latex]W[\/latex], so the area of a rectangle is [latex]A=L\\cdot W[\/latex].<\/p>\n<p>The area of this rectangular rug is [latex]6[\/latex] square feet, its length times its width.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223838\/CNX_BMath_Figure_09_04_013.png\" alt=\"A rectangle is shown. It is made up of 6 squares. The bottom is 2 squares across and marked as 2, the side is 3 squares long and marked as 3.\" \/><\/p>\n<div class=\"textbox shaded\">\n<h3>Properties of Rectangles<\/h3>\n<ul id=\"fs-id1171497076758\">\n<li>Rectangles have four sides and four right [latex]\\left(\\text{90}^ \\circ\\right)[\/latex] angles.<\/li>\n<li>The lengths of opposite sides are equal.<\/li>\n<li>The perimeter, [latex]P[\/latex], of a rectangle is the sum of twice the length and twice the width. See the first image. [latex]P=2L+2W[\/latex]<\/li>\n<li>The area, [latex]A[\/latex], of a rectangle is the length times the width. [latex]A=L\\cdot W[\/latex]<\/li>\n<\/ul>\n<\/div>\n<p>For easy reference as we work the examples in this section, we will restate the Problem Solving Strategy for Geometry Applications here.<\/p>\n<div class=\"textbox shaded\">\n<h3>Use a Problem Solving Strategy for Geometry Applications<\/h3>\n<ol id=\"eip-id1170325029073\" class=\"stepwise\">\n<li><strong>Read<\/strong> the problem and make sure you understand all the words and ideas. Draw the figure and label it with the given information.<\/li>\n<li><strong>Identify<\/strong> what you are looking for.<\/li>\n<li><strong>Name<\/strong> what you are looking for. Choose a variable to represent that quantity.<\/li>\n<li><strong>Translate<\/strong> into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.<\/li>\n<li><strong>Solve<\/strong> the equation using good algebra techniques.<\/li>\n<li><strong>Check<\/strong> the answer in the problem and make sure it makes sense.<\/li>\n<li><strong>Answer<\/strong> the question with a complete sentence.<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>The length of a rectangle is [latex]32[\/latex] meters and the width is [latex]20[\/latex] meters.<\/p>\n<p>1. Find the perimeter<\/p>\n<p>2. Find the area<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168468455627\" class=\"unnumbered unstyled\" summary=\"Step 1 says,\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223840\/CNX_BMath_Figure_09_04_067_img_MW-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td>the perimeter of a rectangle<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let [latex]P[\/latex] = the perimeter<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong>Translate.<\/strong><\/p>\n<p>Write the appropriate formula.<\/p>\n<p>Substitute.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223841\/CNX_BMath_Figure_09_04_067_img_MW-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td>[latex]P=64+40[\/latex]<\/p>\n<p>[latex]P=104[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong><\/p>\n<p>[latex]p\\stackrel{?}{=}104[\/latex]<\/p>\n<p>[latex]20+32+20+32\\stackrel{?}{=}104[\/latex]<\/p>\n<p>[latex]104=104\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td>The perimeter of the rectangle is [latex]104[\/latex] meters.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168467114806\" class=\"unnumbered unstyled\" summary=\"Step 1 says,\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223845\/CNX_BMath_Figure_09_04_068_img_MW-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td>the area of a rectangle<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em>A<\/em> = the area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong>Translate.<\/strong><\/p>\n<p>Write the appropriate formula.<\/p>\n<p>Substitute.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223846\/CNX_BMath_Figure_09_04_068_img_MW-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td>[latex]A=640[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong><\/p>\n<p>[latex]A\\stackrel{?}{=}640[\/latex]<\/p>\n<p>[latex]32\\cdot 20\\stackrel{?}{=}640[\/latex]<\/p>\n<p>[latex]640=640\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td>The area of the rectangle is [latex]640[\/latex] square meters.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146510\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146510&theme=oea&iframe_resize_id=ohm146510&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Find the length of a rectangle with perimeter [latex]50[\/latex] inches and width [latex]10[\/latex] inches.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q172562\">Show Solution<\/span><\/p>\n<div id=\"q172562\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168469470101\" class=\"unnumbered unstyled\" summary=\"Step 1 says,\">\n<tbody>\n<tr>\n<td>Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223850\/CNX_BMath_Figure_09_04_069_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td>the length of the rectangle<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let\u00a0[latex]L[\/latex] = the length<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong>Translate.<\/strong><\/p>\n<p>Write the appropriate formula.<\/p>\n<p>Substitute.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223852\/CNX_BMath_Figure_09_04_069_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td>[latex]50\\color{red}{- 20}=2L+20\\color{red}{- 20}[\/latex]<\/p>\n<p>[latex]30=2L[\/latex]<\/p>\n<p>[latex]{\\Large\\frac{30}{\\color{red}{2}}}={\\Large\\frac{2L}{\\color{red}{2}}}[\/latex]<\/p>\n<p>[latex]15=L[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong><\/p>\n<p>[latex]p=50[\/latex]<\/p>\n<p>[latex]15+10+15+10\\stackrel{?}{=}50[\/latex]<\/p>\n<p>[latex]50=50\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td>The length is [latex]15[\/latex] inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146518\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146518&theme=oea&iframe_resize_id=ohm146518&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the next example, the width is defined in terms of the length. We\u2019ll wait to draw the figure until we write an expression for the width so that we can label one side with that expression.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>The width of a rectangle is two inches less than the length. The perimeter is [latex]52[\/latex] inches. Find the length and width.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q886120\">Show Solution<\/span><\/p>\n<div id=\"q886120\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168466427903\" class=\"unnumbered unstyled\" summary=\"Step 1 says,\" style=\"width: auto;\">\n<tbody>\n<tr>\n<td>Step 1. <strong>Read<\/strong> the problem.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td>the length and width of the rectangle<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/p>\n<p>Now we can draw a figure using these expressions for the length and width.<\/td>\n<td>Since the width is defined in terms of the length, we let <em>L<\/em> = length. The width is two feet less that the length, so we let <em>L<\/em> \u2212 2 = width<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223855\/CNX_BMath_Figure_09_04_070_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong>Translate.<\/strong><\/p>\n<p>Write the appropriate formula. The formula for the perimeter of a rectangle relates all the information.<\/p>\n<p>Substitute in the given information.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223856\/CNX_BMath_Figure_09_04_070_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td>[latex]52=2L+2L - 4[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td>[latex]52=4L - 4[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add [latex]4[\/latex] to each side.<\/td>\n<td>[latex]56=4L[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide by [latex]4[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{56}{4}}={\\Large\\frac{4L}{4}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]14=L[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>The length is [latex]14[\/latex] inches.<\/td>\n<\/tr>\n<tr>\n<td>Now we need to find the width.<\/td>\n<td>\u00a0[latex]L-2[\/latex]<\/p>\n<p>[latex]\\color{red}{14}-2[\/latex]<\/p>\n<p>[latex]12[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The width is [latex]L\u22122[\/latex].<\/td>\n<td>&nbsp;<\/p>\n<p>The width is [latex]12[\/latex] inches.<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong><\/p>\n<p>Since [latex]14+12+14+12=52[\/latex] , this works!<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td>The length is [latex]14[\/latex] feet and the width is [latex]12[\/latex] feet.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146504\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146504&theme=oea&iframe_resize_id=ohm146504&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>The length of a rectangle is four centimeters more than twice the width. The perimeter is [latex]32[\/latex] centimeters. Find the length and width.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q869311\">Show Solution<\/span><\/p>\n<div id=\"q869311\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468670350\" class=\"unnumbered unstyled\" summary=\"Step 1 says,\" style=\"width: auto;\">\n<tbody>\n<tr>\n<td>Step 1. <strong>Read<\/strong> the problem.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td>the length and width<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em>W<\/em> = width<\/p>\n<p>The length is four more than twice the width.<\/p>\n<p>[latex]2w+4[\/latex] = length<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223858\/CNX_BMath_Figure_09_04_071_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong>Translate.<\/strong><\/p>\n<p>Write the appropriate formula and substitute in the given information.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223900\/CNX_BMath_Figure_09_04_071_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td>[latex]32=4w+8+2w[\/latex]<\/p>\n<p>[latex]32=6w+8[\/latex]<\/p>\n<p>[latex]24=6w[\/latex]<\/p>\n<p>[latex]4=w[\/latex] (width)<\/p>\n<p>[latex]2w+4=[\/latex] length<\/p>\n<p>[latex]2(\\color{red}{4})+4[\/latex]<\/p>\n<p>[latex]8+4=12[\/latex]<\/p>\n<p>The length is\u00a0[latex]12[\/latex]cm.<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong><\/p>\n<p>[latex]P=2L+2W[\/latex]<\/p>\n<p>[latex]P\\stackrel{?}{=}2\\cdot 12+2\\cdot 4[\/latex]<\/p>\n<p>[latex]32=32\\quad\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td>The length is [latex]12[\/latex] cm and the width is [latex]4[\/latex] cm.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146521\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146521&theme=oea&iframe_resize_id=ohm146521&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146522\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146522&theme=oea&iframe_resize_id=ohm146522&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Watch this video to see another similar example of finding area given the relationship between the length and width of a rectangle.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex: Find the Area of a Rectangle Given the Perimeter\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/zUlU64Umnq4?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>The area of a rectangular room is [latex]168[\/latex] square feet. The length is [latex]14[\/latex] feet. What is the width?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q247910\">Show Solution<\/span><\/p>\n<div id=\"q247910\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168466072798\" class=\"unnumbered unstyled\" summary=\"Step 1 says,\" style=\"width: auto;\">\n<tbody>\n<tr>\n<td>Step 1. <strong>Read<\/strong> the problem.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223903\/CNX_BMath_Figure_09_04_083_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td>the width of a rectangular room<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <em>W<\/em> = width<\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong>Translate.<\/strong><\/p>\n<p>Write the appropriate formula and substitute in the given information.<\/td>\n<td>[latex]A=LW[\/latex]<\/p>\n<p>[latex]168=14W[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td>[latex]\\Large\\frac{168}{14}\\normalsize=    \\Large\\frac{14W}{14}[\/latex]<\/p>\n<p>[latex]12=W[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong><\/p>\n<p>[latex]A=LW[\/latex]<\/p>\n<p>[latex]168\\stackrel{?}{=}14\\cdot 12[\/latex]<\/p>\n<p>[latex]168=168\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td>The width of the room is [latex]12[\/latex] feet.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146523\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146523&theme=oea&iframe_resize_id=ohm146523&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the next example you will see a similar application involving perimeter, length, and width.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Find the Width of a Rectangle Given the Perimeter \/ Literal Equation\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/jlxPgKQfhQs?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>The perimeter of a rectangular swimming pool is [latex]150[\/latex] feet. The length is [latex]15[\/latex] feet more than the width. Find the length and width.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q207235\">Show Solution<\/span><\/p>\n<div id=\"q207235\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168469520954\" class=\"unnumbered unstyled\" summary=\"Step 1 says,\" style=\"width: auto;\">\n<tbody>\n<tr>\n<td>Step 1. <strong>Read<\/strong> the problem. Draw the figure and label it with the given information.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223907\/CNX_BMath_Figure_09_04_072.img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td>the length and width of the pool<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent it.<\/p>\n<p>The length is [latex]15[\/latex] feet more than the width.<\/td>\n<td>Let [latex]W=\\text{width}[\/latex]<\/p>\n<p>[latex]W+15=\\text{length}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 4.<strong>Translate.<\/strong><\/p>\n<p>Write the appropriate formula and substitute.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223908\/CNX_BMath_Figure_09_04_072_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td>[latex]150=2w+30+2w[\/latex]<\/p>\n<p>[latex]150=4w+30[\/latex]<\/p>\n<p>[latex]120=4w[\/latex]<\/p>\n<p>[latex]30=w[\/latex] the width of the pool.<\/p>\n<p>[latex]w+15[\/latex] the length of the pool.<\/p>\n<p>[latex]\\color{red}{30}+15[\/latex]<\/p>\n<p>[latex]45[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong><\/p>\n<p>[latex]P=2L+2W[\/latex]<\/p>\n<p>[latex]150\\stackrel{?}{=}2(45)+2(30)[\/latex]<\/p>\n<p>[latex]150=150\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td>The length of the pool is [latex]45[\/latex] feet and the width is [latex]30[\/latex] feet.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146524\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146524&theme=oea&iframe_resize_id=ohm146524&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-4446\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID 146524, 146522, 146518, 146504. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex: Find the Area of a Rectangle Given the Perimeter. <strong>Authored by<\/strong>: James Sousa (amthispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/zUlU64Umnq4\">https:\/\/youtu.be\/zUlU64Umnq4<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Find the Width of a Rectangle Given the Perimeter \/ Literal Equation. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/jlxPgKQfhQs\">https:\/\/youtu.be\/jlxPgKQfhQs<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":25777,"menu_order":6,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"original\",\"description\":\"Question ID 146524, 146522, 146518, 146504\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Find the Area of a Rectangle Given the 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(mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/jlxPgKQfhQs\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4446","chapter","type-chapter","status-web-only","hentry"],"part":3706,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4446","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4446\/revisions"}],"predecessor-version":[{"id":4447,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4446\/revisions\/4447"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/3706"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4446\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=4446"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=4446"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=4446"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=4446"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}