{"id":257551,"date":"2025-07-17T14:20:33","date_gmt":"2025-07-17T14:20:33","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=257551"},"modified":"2025-07-17T14:20:35","modified_gmt":"2025-07-17T14:20:35","slug":"the-area-of-a-rectangle-is-48-square-feet","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/17\/the-area-of-a-rectangle-is-48-square-feet\/","title":{"rendered":"The area of a rectangle is 48 square feet."},"content":{"rendered":"\n

The area of a rectangle is 48 square feet. The length is 8 feet longer than the width. 1) Which picture corresponds to the problem? 2) What are the dimensions of the rectangle?<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Which picture corresponds to the problem?<\/h3>\n\n\n\n

For this, we’d expect a rectangle where one side (the length) is 8 feet longer than the other side (the width). While I can’t generate the picture, imagine a rectangular shape, and label the length LLL and the width WWW. The relationship given is:L=W+8L = W + 8L=W+8<\/p>\n\n\n\n

So the length is 8 feet longer than the width, and the area of the rectangle is A=48A = 48A=48 square feet.<\/p>\n\n\n\n

2) What are the dimensions of the rectangle?<\/h3>\n\n\n\n

We know that:Area=Length\u00d7Width\\text{Area} = \\text{Length} \\times \\text{Width}Area=Length\u00d7Width<\/p>\n\n\n\n

Given that the area is 48 square feet, we can write the equation:L\u00d7W=48L \\times W = 48L\u00d7W=48<\/p>\n\n\n\n

Substitute L=W+8L = W + 8L=W+8 into the equation:(W+8)\u00d7W=48(W + 8) \\times W = 48(W+8)\u00d7W=48<\/p>\n\n\n\n

Now expand the equation:W2+8W=48W^2 + 8W = 48W2+8W=48<\/p>\n\n\n\n

Rearrange the equation to form a quadratic equation:W2+8W\u221248=0W^2 + 8W – 48 = 0W2+8W\u221248=0<\/p>\n\n\n\n

Now, solve for WWW using the quadratic formula:W=\u2212b\u00b1b2\u22124ac2aW = \\frac{-b \\pm \\sqrt{b^2 – 4ac}}{2a}W=2a\u2212b\u00b1b2\u22124ac\u200b\u200b<\/p>\n\n\n\n

Where a=1a = 1a=1, b=8b = 8b=8, and c=\u221248c = -48c=\u221248. Plug these values into the quadratic formula:W=\u22128\u00b182\u22124(1)(\u221248)2(1)W = \\frac{-8 \\pm \\sqrt{8^2 – 4(1)(-48)}}{2(1)}W=2(1)\u22128\u00b182\u22124(1)(\u221248)\u200b\u200bW=\u22128\u00b164+1922W = \\frac{-8 \\pm \\sqrt{64 + 192}}{2}W=2\u22128\u00b164+192\u200b\u200bW=\u22128\u00b12562W = \\frac{-8 \\pm \\sqrt{256}}{2}W=2\u22128\u00b1256\u200b\u200bW=\u22128\u00b1162W = \\frac{-8 \\pm 16}{2}W=2\u22128\u00b116\u200b<\/p>\n\n\n\n

This gives us two possible solutions:W=\u22128+162=4orW=\u22128\u2212162=\u221212W = \\frac{-8 + 16}{2} = 4 \\quad \\text{or} \\quad W = \\frac{-8 – 16}{2} = -12W=2\u22128+16\u200b=4orW=2\u22128\u221216\u200b=\u221212<\/p>\n\n\n\n

Since width cannot be negative, we choose W=4W = 4W=4 feet.<\/p>\n\n\n\n

Now, substitute W=4W = 4W=4 into the equation L=W+8L = W + 8L=W+8:L=4+8=12\u2009feetL = 4 + 8 = 12 \\, \\text{feet}L=4+8=12feet<\/p>\n\n\n\n

Final Answer:<\/h3>\n\n\n\n
    \n
  • The width of the rectangle is 4 feet<\/strong>.<\/li>\n\n\n\n
  • The length of the rectangle is 12 feet<\/strong>.<\/li>\n<\/ul>\n\n\n\n

    Thus, the dimensions of the rectangle are 12 feet by 4 feet.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    The area of a rectangle is 48 square feet. The length is 8 feet longer than the width. 1) Which picture corresponds to the problem? 2) What are the dimensions of the rectangle? The Correct Answer and Explanation is: Which picture corresponds to the problem? For this, we’d expect a rectangle where one side (the […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-257551","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/257551","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=257551"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/257551\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=257551"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=257551"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=257551"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}