{"id":262945,"date":"2025-07-20T23:23:03","date_gmt":"2025-07-20T23:23:03","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=262945"},"modified":"2025-07-20T23:23:05","modified_gmt":"2025-07-20T23:23:05","slug":"the-two-triangles-in-the-diagram-are-similar-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/20\/the-two-triangles-in-the-diagram-are-similar-2\/","title":{"rendered":"The two triangles in the diagram are similar."},"content":{"rendered":"\n<p>1 The two triangles in the diagram are similar. A x cm B 2 cm E C 9 cm D 3 cm There are two possible values of x. Work out each of these values. State any assumptions you make in your working. (5 marks) Adapted from IMAI\/IH, November 2017, Q22<\/p>\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>To solve this problem, we need to apply the concept of similar triangles. When two triangles are similar, their corresponding sides are proportional. From the information given, we know the following:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Triangle ABC is similar to triangle CDE.<\/li>\n\n\n\n<li>The sides of triangle ABC are proportional to the sides of triangle CDE.<\/li>\n\n\n\n<li>We are given that side <strong>AB<\/strong> = <strong>x<\/strong> cm, <strong>BC<\/strong> = 2 cm, <strong>CD<\/strong> = 9 cm, and <strong>DE<\/strong> = 3 cm.<\/li>\n<\/ul>\n\n\n\n<p>We can set up a proportion based on the similarity of the triangles. The corresponding sides of the triangles will be in the same ratio:ABCD=BCDE\\frac{{AB}}{{CD}} = \\frac{{BC}}{{DE}}CDAB\u200b=DEBC\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Write the proportion<\/h3>\n\n\n\n<p>Using the values provided, we can substitute into the proportion:x9=23\\frac{{x}}{{9}} = \\frac{{2}}{{3}}9x\u200b=32\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Solve for <strong>x<\/strong><\/h3>\n\n\n\n<p>To solve for <strong>x<\/strong>, we can cross-multiply and solve:x\u00d73=2\u00d79x \\times 3 = 2 \\times 9x\u00d73=2\u00d793x=183x = 183x=18x=183=6\u2009cmx = \\frac{{18}}{{3}} = 6 \\, \\text{cm}x=318\u200b=6cm<\/p>\n\n\n\n<p>This gives one possible value for <strong>x<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Consider the reverse ratio<\/h3>\n\n\n\n<p>Since the triangles are similar, we also know that the sides can be related by the reverse proportion:CDAB=DEBC\\frac{{CD}}{{AB}} = \\frac{{DE}}{{BC}}ABCD\u200b=BCDE\u200b<\/p>\n\n\n\n<p>Substitute the known values:9x=32\\frac{{9}}{{x}} = \\frac{{3}}{{2}}x9\u200b=23\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Solve for <strong>x<\/strong> again<\/h3>\n\n\n\n<p>Cross-multiply to find <strong>x<\/strong>:9\u00d72=3\u00d7x9 \\times 2 = 3 \\times x9\u00d72=3\u00d7x18=3&#215;18 = 3&#215;18=3xx=183=6\u2009cmx = \\frac{{18}}{{3}} = 6 \\, \\text{cm}x=318\u200b=6cm<\/p>\n\n\n\n<p>Thus, the only possible value for <strong>x<\/strong> is <strong>6 cm<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>In this case, we find that <strong>x = 6 cm<\/strong>. The assumption we made was that the triangles are indeed similar and that their corresponding sides are proportional.<\/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\/learnexams-banner6-1269.jpeg\" alt=\"\" class=\"wp-image-262946\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>1 The two triangles in the diagram are similar. A x cm B 2 cm E C 9 cm D 3 cm There are two possible values of x. Work out each of these values. State any assumptions you make in your working. (5 marks) Adapted from IMAI\/IH, November 2017, Q22 The Correct Answer and [&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-262945","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/262945","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=262945"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/262945\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=262945"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=262945"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=262945"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}