Which is a true statement about a 45-45-90 triangle? <\/p>\n\n\n\n
A. Each leg is 3 times as long as the hypotenuse. <\/p>\n\n\n\n
B. Each leg is 12 times as long as the hypotenuse. <\/p>\n\n\n\n
C. The hypotenuse is 3 times as long as either leg. <\/p>\n\n\n\n
D. The hypotenuse is v2 times as long as either leg.<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n The correct answer is:<\/p>\n\n\n\n D. The hypotenuse is \u221a2 times as long as either leg.<\/strong><\/p>\n\n\n\n A 45-45-90 triangle is a special type of isosceles right triangle where the two legs are equal in length, and the angles are 45\u00b0, 45\u00b0, and 90\u00b0. The relationship between the sides of a 45-45-90 triangle can be derived from the properties of right triangles and the Pythagorean theorem.<\/p>\n\n\n\n Let\u2019s assume the length of each leg of the triangle is x<\/strong>. According to the Pythagorean theorem: x2+x2=hypotenuse2x^2 + x^2 = \\text{hypotenuse}^2<\/p>\n\n\n\n Simplifying this gives: 2×2=hypotenuse22x^2 = \\text{hypotenuse}^2<\/p>\n\n\n\n Taking the square root of both sides: hypotenuse=x2\\text{hypotenuse} = x\\sqrt{2}<\/p>\n\n\n\n Thus, the length of the hypotenuse is \u221a2 times the length of either leg<\/strong>.<\/p>\n\n\n\n This relationship is key to understanding 45-45-90 triangles. If the legs are of length x<\/strong>, the hypotenuse will always be x\u221a2<\/strong>.<\/p>\n\n\n\n To clarify the options:<\/p>\n\n\n\n This ratio holds true regardless of the size of the triangle, making the 45-45-90 triangle a useful model for problems involving angles and distances in geometry.<\/p>\n","protected":false},"excerpt":{"rendered":" Which is a true statement about a 45-45-90 triangle? A. Each leg is 3 times as long as the hypotenuse. B. Each leg is 12 times as long as the hypotenuse. C. The hypotenuse is 3 times as long as either leg. D. The hypotenuse is v2 times as long as either leg. The correct […]<\/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-242133","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/242133","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=242133"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/242133\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=242133"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=242133"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=242133"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation:<\/h3>\n\n\n\n
\n