{"id":266072,"date":"2025-07-22T15:36:05","date_gmt":"2025-07-22T15:36:05","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=266072"},"modified":"2025-07-22T15:36:07","modified_gmt":"2025-07-22T15:36:07","slug":"the-pythagorean-theorem","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/22\/the-pythagorean-theorem\/","title":{"rendered":"The Pythagorean Theorem"},"content":{"rendered":"\n<p>Calculator 6.11 Unit Test: The Pythagorean Theorem &#8211; Part 1 Determine whether each set of side lengths could be the sides of a right triangle. Drag and drop each set of side lengths to the correct box. Right Triangle 8 in., 15 in., 17 in. 4 in., 15 in., 17 in. Not a Right Triangle 1 2 3 4 5 6 7 8 9<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-642.png\" alt=\"\" class=\"wp-image-266073\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Here is the correct answer and explanation for the problem.<\/p>\n\n\n\n<p><strong>Correct Answer<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Right Triangle:<\/strong>\u00a08 in., 15 in., 17 in.<\/li>\n\n\n\n<li><strong>Not a Right Triangle:<\/strong>\u00a04 in., 15 in., 17 in.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation<\/strong><\/h3>\n\n\n\n<p>To determine if a set of side lengths can form a right triangle, we use the converse of the Pythagorean theorem. This theorem states that if the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. The formula is expressed as a\u00b2 + b\u00b2 = c\u00b2, where &#8216;a&#8217; and &#8216;b&#8217; are the lengths of the two shorter sides (the legs), and &#8216;c&#8217; is the length of the longest side (the hypotenuse).<\/p>\n\n\n\n<p>Let&#8217;s test the first set of side lengths: 8 in., 15 in., 17 in.<br>In this set, the longest side is 17 inches, so we will assign it as &#8216;c&#8217;. The other two sides, 8 inches and 15 inches, will be &#8216;a&#8217; and &#8216;b&#8217;.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Let a = 8, b = 15, and c = 17.<\/li>\n\n\n\n<li>Now, we check if a\u00b2 + b\u00b2 = c\u00b2.<\/li>\n\n\n\n<li>Calculate the sum of the squares of the two shorter sides: 8\u00b2 + 15\u00b2 = 64 + 225 = 289.<\/li>\n\n\n\n<li>Calculate the square of the longest side: 17\u00b2 = 289.<\/li>\n\n\n\n<li>Since 289 equals 289, the equation a\u00b2 + b\u00b2 = c\u00b2 is true. Therefore, the side lengths 8 in., 15 in., and 17 in. form a right triangle.<\/li>\n<\/ul>\n\n\n\n<p>Next, let&#8217;s test the second set of side lengths: 4 in., 15 in., 17 in.<br>Again, the longest side is 17 inches, which will be our &#8216;c&#8217;. The other two sides are 4 inches and 15 inches.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Let a = 4, b = 15, and c = 17.<\/li>\n\n\n\n<li>We check if a\u00b2 + b\u00b2 = c\u00b2.<\/li>\n\n\n\n<li>Calculate the sum of the squares of the two shorter sides: 4\u00b2 + 15\u00b2 = 16 + 225 = 241.<\/li>\n\n\n\n<li>Calculate the square of the longest side: 17\u00b2 = 289.<\/li>\n\n\n\n<li>In this case, 241 does not equal 289. The equation a\u00b2 + b\u00b2 = c\u00b2 is false. Consequently, the side lengths 4 in., 15 in., and 17 in. cannot form a right triangle.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1534.jpeg\" alt=\"\" class=\"wp-image-266078\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Calculator 6.11 Unit Test: The Pythagorean Theorem &#8211; Part 1 Determine whether each set of side lengths could be the sides of a right triangle. Drag and drop each set of side lengths to the correct box. Right Triangle 8 in., 15 in., 17 in. 4 in., 15 in., 17 in. Not a Right Triangle [&hellip;]<\/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-266072","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/266072","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=266072"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/266072\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=266072"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=266072"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=266072"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}