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.<\/p>\n\n\n\n
The correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To determine the possible dimensions of the base of the doghouse, we can represent the width of the doghouse as ( x ), and the length as ( x + 4 ), since the problem states that the length is 4 feet more than the width. The area of the base of the doghouse is given as 21 square feet.<\/p>\n\n\n\n The area of a rectangle is calculated by multiplying the length and width, so we can set up the following equation:<\/p>\n\n\n\n [ Substitute the known values:<\/p>\n\n\n\n [ Now, expand the equation:<\/p>\n\n\n\n [ To write the equation in standard form, we subtract 21 from both sides:<\/p>\n\n\n\n [ This is a quadratic equation in the form ( ax^2 + bx + c = 0 ), where ( a = 1 ), ( b = 4 ), and ( c = -21 ).<\/p>\n\n\n\n The quadratic equation ( x^2 + 4x – 21 = 0 ) represents the relationship between the width ( x ) and the given area of the rectangular base of the doghouse. In this equation, ( x ) is the width, and the length is ( x + 4 ), which reflects the condition that the length is 4 feet more than the width.<\/p>\n\n\n\n This problem essentially asks you to apply the formula for the area of a rectangle to a situation where the length and width are related. By expressing the length in terms of the width and plugging this into the area formula, you obtain a quadratic equation. Solving this quadratic equation will give the possible values of ( x ), the width of the doghouse. Once you have the width, you can easily determine the corresponding length by adding 4 to the width.<\/p>\n\n\n\n In practical terms, solving this quadratic equation helps Jason figure out the possible dimensions of the doghouse\u2019s base, ensuring that the total area remains 21 square feet.<\/p>\n","protected":false},"excerpt":{"rendered":" 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 […]<\/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-151140","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/151140","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=151140"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/151140\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=151140"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=151140"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=151140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\\text{Area} = \\text{Length} \\times \\text{Width}
]<\/p>\n\n\n\n
21 = (x + 4) \\times x
]<\/p>\n\n\n\n
21 = x(x + 4)
]
[
21 = x^2 + 4x
]<\/p>\n\n\n\n
x^2 + 4x – 21 = 0
]<\/p>\n\n\n\nExplanation<\/h3>\n\n\n\n