{"id":166880,"date":"2024-11-14T15:03:43","date_gmt":"2024-11-14T15:03:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=166880"},"modified":"2024-11-14T15:03:45","modified_gmt":"2024-11-14T15:03:45","slug":"joan-is-building-a-sandbox-in-the-shape-of-a-regular-pentagon","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/14\/joan-is-building-a-sandbox-in-the-shape-of-a-regular-pentagon\/","title":{"rendered":"Joan is building a sandbox in the shape of a regular pentagon."},"content":{"rendered":"\n

Joan is building a sandbox in the shape of a regular pentagon. the perimeter of the pentagon is 35y4 \u2013 65×3 inches. what is the length of one side of the sandbox?<\/p>\n\n\n\n

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

To find the length of one side of a regular pentagon with a perimeter of (35y^4 – 65x^3) inches, we can divide the perimeter by 5, since a regular pentagon has five equal sides.<\/p>\n\n\n\n

Step-by-Step Solution<\/h3>\n\n\n\n
    \n
  1. Given perimeter<\/strong>: The perimeter of the pentagon is (35y^4 – 65x^3).<\/li>\n\n\n\n
  2. Number of sides<\/strong>: A pentagon has five sides, so each side will be one-fifth of the total perimeter.<\/li>\n\n\n\n
  3. Dividing the expression<\/strong>: We divide the perimeter expression by 5 to find the length of one side: [
    \\text{Length of one side} = \\frac{35y^4 – 65x^3}{5}
    ]<\/li>\n\n\n\n
  4. Simplify each term<\/strong>:<\/li>\n<\/ol>\n\n\n\n
      \n
    • For the term (35y^4): (\\frac{35y^4}{5} = 7y^4).<\/li>\n\n\n\n
    • For the term (-65x^3): (\\frac{-65x^3}{5} = -13x^3). Therefore: [
      \\text{Length of one side} = 7y^4 – 13x^3
      ]<\/li>\n<\/ul>\n\n\n\n

      Final Answer<\/h3>\n\n\n\n

      The length of one side of the sandbox is (7y^4 – 13x^3) inches.<\/p>\n\n\n\n

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

      In geometry, a regular polygon is a shape with all sides and angles equal. For a regular pentagon, this means each of its five sides has the same length. When given the perimeter of a regular polygon, we can determine the length of one side by dividing the total perimeter by the number of sides. This works because dividing evenly ensures each segment represents a side length.<\/p>\n\n\n\n

      In this case, the algebraic expression (35y^4 – 65x^3) represents the perimeter in terms of variables. Dividing each term of this expression by 5 distributes the calculation across each term, resulting in (7y^4 – 13x^3), which is the length of one side.<\/p>\n\n\n\n

      This process of dividing and simplifying terms applies to any algebraic perimeter of a regular polygon; each side length will be the perimeter divided by the number of sides, simplified term-by-term.<\/p>\n","protected":false},"excerpt":{"rendered":"

      Joan is building a sandbox in the shape of a regular pentagon. the perimeter of the pentagon is 35y4 \u2013 65×3 inches. what is the length of one side of the sandbox? The Correct Answer and Explanation is: To find the length of one side of a regular pentagon with a perimeter of (35y^4 – […]<\/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-166880","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/166880","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=166880"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/166880\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=166880"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=166880"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=166880"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}