{"id":243226,"date":"2025-07-04T13:06:40","date_gmt":"2025-07-04T13:06:40","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=243226"},"modified":"2025-07-04T13:06:42","modified_gmt":"2025-07-04T13:06:42","slug":"explain-her-error-and-include-the-correct-expression-for-the-perimeter","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/04\/explain-her-error-and-include-the-correct-expression-for-the-perimeter\/","title":{"rendered":"Explain her error, and include the correct expression for the perimeter"},"content":{"rendered":"\n
    \n
  1. Explain her error, and include the correct expression for the perimeter. The width is (5\/6x + 23) and the height is 12.
    Michelle simplified an expression for the perimeter of the rectangle below and got (5\/6x + 23) + (5\/6x + 23) + 12. Explain her error, and include the correct expression for the perimeter. The width is (5\/6x + 23) and the height is 12.<\/li>\n<\/ol>\n\n\n\n

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

    Michelle made an error in simplifying the expression for the perimeter of the rectangle.<\/p>\n\n\n\n

    The formula for the perimeter of a rectangle is: P=2\u00d7width+2\u00d7heightP = 2 \\times \\text{width} + 2 \\times \\text{height}P=2\u00d7width+2\u00d7height<\/p>\n\n\n\n

    In this case, the width is given as (56x+23)\\left( \\frac{5}{6}x + 23 \\right)(65\u200bx+23) and the height is given as 12. Therefore, the correct expression for the perimeter should be: P=2\u00d7(56x+23)+2\u00d712P = 2 \\times \\left( \\frac{5}{6}x + 23 \\right) + 2 \\times 12P=2\u00d7(65\u200bx+23)+2\u00d712<\/p>\n\n\n\n

    Now, let’s break it down:<\/p>\n\n\n\n

      \n
    1. Multiply the width by 2:<\/li>\n<\/ol>\n\n\n\n

      2\u00d7(56x+23)=106x+46=53x+462 \\times \\left( \\frac{5}{6}x + 23 \\right) = \\frac{10}{6}x + 46 = \\frac{5}{3}x + 462\u00d7(65\u200bx+23)=610\u200bx+46=35\u200bx+46<\/p>\n\n\n\n

        \n
      1. Multiply the height by 2:<\/li>\n<\/ol>\n\n\n\n

        2\u00d712=242 \\times 12 = 242\u00d712=24<\/p>\n\n\n\n

        So, the correct expression for the perimeter is: P=53x+46+24P = \\frac{5}{3}x + 46 + 24P=35\u200bx+46+24<\/p>\n\n\n\n

          \n
        1. Combine the constant terms:<\/li>\n<\/ol>\n\n\n\n

          P=53x+70P = \\frac{5}{3}x + 70P=35\u200bx+70<\/p>\n\n\n\n

          Explanation of Michelle\u2019s error:<\/strong><\/p>\n\n\n\n

          Michelle mistakenly simplified the perimeter expression as: (56x+23)+(56x+23)+12\\left( \\frac{5}{6}x + 23 \\right) + \\left( \\frac{5}{6}x + 23 \\right) + 12(65\u200bx+23)+(65\u200bx+23)+12<\/p>\n\n\n\n

          This is incorrect because she did not account for the full perimeter formula. Instead of multiplying the width by 2 and the height by 2, she added the width twice and added the height only once. The correct approach requires multiplying both the width and height by 2 before summing them to find the perimeter.<\/p>\n\n\n\n

          Thus, the correct perimeter expression is: P=53x+70P = \\frac{5}{3}x + 70P=35\u200bx+70<\/p>\n\n\n\n

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

          The Correct Answer and Explanation is: Michelle made an error in simplifying the expression for the perimeter of the rectangle. The formula for the perimeter of a rectangle is: P=2\u00d7width+2\u00d7heightP = 2 \\times \\text{width} + 2 \\times \\text{height}P=2\u00d7width+2\u00d7height In this case, the width is given as (56x+23)\\left( \\frac{5}{6}x + 23 \\right)(65\u200bx+23) and the height is […]<\/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-243226","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/243226","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=243226"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/243226\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=243226"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=243226"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=243226"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}