{"id":234791,"date":"2025-06-14T13:06:06","date_gmt":"2025-06-14T13:06:06","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=234791"},"modified":"2025-06-14T13:06:07","modified_gmt":"2025-06-14T13:06:07","slug":"triangle-fgh-is-a-right-triangle","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/14\/triangle-fgh-is-a-right-triangle\/","title":{"rendered":"Triangle FGH is a right triangle."},"content":{"rendered":"\n<p>Triangle FGH is a right triangle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/image-498.png\" alt=\"\" class=\"wp-image-234792\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>A. True<\/strong><\/p>\n\n\n\n<p>To determine if \u0394FGH is a right triangle, the converse of the Pythagorean theorem must be applied. This theorem states that if a triangle&#8217;s side lengths satisfy the equation a\u00b2 + b\u00b2 = c\u00b2, where &#8216;c&#8217; is the length of the longest side, then the triangle is a right triangle.<\/p>\n\n\n\n<p>First, let&#8217;s identify the lengths of the three sides of the triangle from the image:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Side FH has a length of 7.<\/li>\n\n\n\n<li>Side GH has a length of \u221a51.<\/li>\n\n\n\n<li>Side FG has a length of 10.<\/li>\n<\/ul>\n\n\n\n<p>The longest side of the triangle is FG, with a length of 10. If this is a right triangle, FG must be the hypotenuse. The other two sides, FH and GH, would be the legs.<\/p>\n\n\n\n<p>Next, substitute these lengths into the Pythagorean formula (a\u00b2 + b\u00b2 = c\u00b2):<br>(FH)\u00b2 + (GH)\u00b2 = (FG)\u00b2<br>7\u00b2 + (\u221a51)\u00b2 = 10\u00b2<\/p>\n\n\n\n<p>Now, calculate the square of each value:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>7\u00b2 equals 7 \u00d7 7, which is 49.<\/li>\n\n\n\n<li>(\u221a51)\u00b2 equals 51, as squaring a square root cancels it out.<\/li>\n\n\n\n<li>10\u00b2 equals 10 \u00d7 10, which is 100.<\/li>\n<\/ul>\n\n\n\n<p>Let&#8217;s check if the equation is balanced with these calculated values:<br>49 + 51 = 100<br>100 = 100<\/p>\n\n\n\n<p>The sum of the squares of the two shorter sides (49 + 51) is exactly equal to the square of the longest side (100). Because this relationship holds true, the triangle satisfies the conditions of the converse of the Pythagorean theorem. Therefore, the statement that \u0394FGH is a right triangle is correct. The right angle is at vertex H, which is opposite the longest side (the hypotenuse FG).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-495.jpeg\" alt=\"\" class=\"wp-image-234793\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Triangle FGH is a right triangle. The Correct Answer and Explanation is: A. True To determine if \u0394FGH is a right triangle, the converse of the Pythagorean theorem must be applied. This theorem states that if a triangle&#8217;s side lengths satisfy the equation a\u00b2 + b\u00b2 = c\u00b2, where &#8216;c&#8217; is the length of the [&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-234791","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234791","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=234791"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234791\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=234791"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=234791"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=234791"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}