{"id":226098,"date":"2025-06-04T20:56:50","date_gmt":"2025-06-04T20:56:50","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=226098"},"modified":"2025-06-04T20:56:52","modified_gmt":"2025-06-04T20:56:52","slug":"type-the-correct-answer-in-the-box-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/type-the-correct-answer-in-the-box-2\/","title":{"rendered":"Type the correct answer in the box"},"content":{"rendered":"\n

Type the correct answer in the box. Jason builds doghouses for a pet store. Each doghouse is a wooden structure with a rectangular base that has an area of 21 square feet and a length that is 4 feet more than its width. If x represents the width of the doghouse, write an equation in the given form that can be used to determine the possible dimensions of the base of the doghouse. ax\\textsuperscript{2} + bx = c<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

Correct Answer:<\/h3>\n\n\n\n

The correct equation in the form ax2+bx=cax^2 + bx = c is: x2+4x=21x^2 + 4x = 21<\/p>\n\n\n\n

\n\n\n\n

Explanation <\/h3>\n\n\n\n

This problem involves forming a quadratic equation based on a real-world geometric situation.<\/p>\n\n\n\n

Jason builds doghouses that have rectangular bases. We’re told:<\/p>\n\n\n\n

    \n
  • The area<\/strong> of each base is 21 square feet.<\/li>\n\n\n\n
  • The length<\/strong> is 4 feet more than the width<\/strong>.<\/li>\n\n\n\n
  • We’re asked to write an equation in the form ax2+bx=cax^2 + bx = c, where xx is the width.<\/li>\n<\/ul>\n\n\n\n

    Let’s break it down step-by-step:<\/p>\n\n\n\n

      \n
    1. Assign variables<\/strong>:
      Let xx be the width of the rectangular base (in feet).<\/li>\n\n\n\n
    2. Express length in terms of width<\/strong>:
      The length is 4 feet more than the width, so the length is x+4x + 4.<\/li>\n\n\n\n
    3. Use the area formula<\/strong>:
      The area of a rectangle is given by: Area=Length\u00d7Width\\text{Area} = \\text{Length} \\times \\text{Width} Substituting the known values: 21=x(x+4)21 = x(x + 4)<\/li>\n\n\n\n
    4. Simplify the equation<\/strong>:
      Multiply the expression: 21=x2+4×21 = x^2 + 4x<\/li>\n\n\n\n
    5. Rearrange into standard form<\/strong>:
      Bring all terms to one side to match the form ax2+bx=cax^2 + bx = c. Since the prompt asks for the equation in the form<\/strong> ax2+bx=cax^2 + bx = c, we don\u2019t need to rearrange further. We can write: x2+4x=21x^2 + 4x = 21<\/li>\n<\/ol>\n\n\n\n

      This equation now models the situation: any solution for xx will give the width of a possible doghouse base that meets the criteria. From there, x+4x + 4 gives the length.<\/p>\n\n\n\n

      In summary, by translating the word problem into mathematical expressions and applying the formula for area, we derived a quadratic equation that can be used to determine the possible width of the doghouse base.<\/p>\n\n\n\n

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

      Type the correct answer in the box. Jason builds doghouses for a pet store. Each doghouse is a wooden structure with a rectangular base that has an area of 21 square feet and a length that is 4 feet more than its width. If x represents the width of the doghouse, write an equation in […]<\/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-226098","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226098","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=226098"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/226098\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=226098"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=226098"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=226098"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}