{"id":272949,"date":"2025-07-27T08:03:45","date_gmt":"2025-07-27T08:03:45","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=272949"},"modified":"2025-07-27T08:03:47","modified_gmt":"2025-07-27T08:03:47","slug":"what-is-the-relationship-between-the-length-of-the-hypotenuse-and-the-length-of-the-legs-in-a-45-45-90-triangle","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/27\/what-is-the-relationship-between-the-length-of-the-hypotenuse-and-the-length-of-the-legs-in-a-45-45-90-triangle\/","title":{"rendered":"What is the relationship between the length of the hypotenuse and the length of the legs in a 45 &#8211; 45 &#8211; 90 triangle"},"content":{"rendered":"\n<p>What is the relationship between the length of the hypotenuse and the length of the legs in a 45 &#8211; 45 &#8211; 90 triangle?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>In a 45-45-90 triangle, the two legs are of equal length, and the hypotenuse is related to the length of the legs in a specific way. The relationship is that the length of the hypotenuse is <strong>\u221a2 times<\/strong> the length of each leg.<\/p>\n\n\n\n<p>This type of triangle is an <strong>isosceles right triangle<\/strong>, meaning the two non-hypotenuse sides (the legs) are congruent. In such a triangle, the angles between the legs are both 45 degrees. This symmetry leads to a special geometric ratio.<\/p>\n\n\n\n<p>To derive this relationship, consider the Pythagorean theorem, which states that in any right triangle: a2+b2=c2a^2 + b^2 = c^2<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>aa and bb are the lengths of the legs.<\/li>\n\n\n\n<li>cc is the length of the hypotenuse.<\/li>\n<\/ul>\n\n\n\n<p>In a 45-45-90 triangle, both legs have the same length, so we can denote them as xx. The Pythagorean theorem then becomes: x2+x2=c2x^2 + x^2 = c^2<\/p>\n\n\n\n<p>Simplifying: 2&#215;2=c22x^2 = c^2<\/p>\n\n\n\n<p>Taking the square root of both sides: 2&#215;2=c2\\sqrt{2x^2} = \\sqrt{c^2} c=x2c = x\\sqrt{2}<\/p>\n\n\n\n<p>Thus, the length of the hypotenuse cc is equal to the length of a leg xx multiplied by 2\\sqrt{2}.<\/p>\n\n\n\n<p>For example, if the length of each leg in a 45-45-90 triangle is 5 units, then the hypotenuse will be: c=52\u22487.07\u2009units.c = 5\\sqrt{2} \\approx 7.07 \\, \\text{units}.<\/p>\n\n\n\n<p>This relationship is crucial when working with 45-45-90 triangles, as it allows you to easily find one side if you know the other, making it a very efficient and predictable type of right triangle in geometry.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is the relationship between the length of the hypotenuse and the length of the legs in a 45 &#8211; 45 &#8211; 90 triangle? The correct answer and explanation is: In a 45-45-90 triangle, the two legs are of equal length, and the hypotenuse is related to the length of the legs in a specific [&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-272949","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/272949","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=272949"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/272949\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=272949"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=272949"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=272949"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}