{"id":35776,"date":"2025-06-24T16:24:02","date_gmt":"2025-06-24T16:24:02","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=35776"},"modified":"2025-06-24T16:24:04","modified_gmt":"2025-06-24T16:24:04","slug":"the-lengths-of-sides-xy-yz-and-xz-of-triangle-xyz-are-7-cm-12-cm-and-15-cm-respectively","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/the-lengths-of-sides-xy-yz-and-xz-of-triangle-xyz-are-7-cm-12-cm-and-15-cm-respectively\/","title":{"rendered":"The lengths of sides XY, YZ, and XZ of triangle XYZ are 7 cm, 12 cm, and 15 cm respectively."},"content":{"rendered":"\n<p>The lengths of sides XY, YZ, and XZ of triangle XYZ are 7 cm, 12 cm, and 15 cm respectively. What angle of the triangle has the largest measure? A. Angle X B. Angle Z C. Angle Y D. Cannot be determined What is the shortest side of triangle PQR if m(P) = 65 and m(LQ) = 58? A. PQ B. PR C. QR D. RP<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Correct Answers:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Angle with the largest measure in triangle XYZ:<\/strong> <strong>C. Angle Y<\/strong><\/li>\n\n\n\n<li><strong>Shortest side of triangle PQR:<\/strong> <strong>C. QR<\/strong><\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Question 1: Triangle XYZ<\/strong><\/h4>\n\n\n\n<p>You are given the lengths of all three sides:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>XY = 7 cm<\/li>\n\n\n\n<li>YZ = 12 cm<\/li>\n\n\n\n<li>XZ = 15 cm<\/li>\n<\/ul>\n\n\n\n<p>In any triangle, the <strong>angle opposite the longest side<\/strong> is the <strong>largest angle<\/strong>.<br>Here, the longest side is <strong>XZ = 15 cm<\/strong>, so the angle <strong>opposite XZ<\/strong> is <strong>Angle Y<\/strong>.<\/p>\n\n\n\n<p>Therefore, the <strong>largest angle is Angle Y<\/strong>, and the correct answer is:<br><strong>C. Angle Y<\/strong><\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Question 2: Triangle PQR<\/strong><\/h4>\n\n\n\n<p>You are given the measures of two angles:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>m\u2220P = 65\u00b0<\/li>\n\n\n\n<li>m\u2220Q = 58\u00b0<\/li>\n<\/ul>\n\n\n\n<p>To find the third angle, use the triangle angle sum property:<br>Sum of angles in any triangle = 180\u00b0<br>So,<br>m\u2220R = 180\u00b0 \u2212 (65\u00b0 + 58\u00b0) = 57\u00b0<\/p>\n\n\n\n<p>Now compare the angle measures:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>m\u2220P = 65\u00b0<\/li>\n\n\n\n<li>m\u2220Q = 58\u00b0<\/li>\n\n\n\n<li>m\u2220R = 57\u00b0<\/li>\n<\/ul>\n\n\n\n<p>In any triangle, the <strong>shortest side is opposite the smallest angle<\/strong>.<br>The smallest angle here is <strong>Angle R = 57\u00b0<\/strong>, so the <strong>shortest side is opposite to Angle R<\/strong>, which is side <strong>PQ<\/strong>.<\/p>\n\n\n\n<p>But wait \u2014 that seems off.<br><strong>Angle R = 57\u00b0<\/strong> \u2192 side opposite is <strong>PQ<\/strong><br><strong>Angle Q = 58\u00b0<\/strong> \u2192 side opposite is <strong>PR<\/strong><br><strong>Angle P = 65\u00b0<\/strong> \u2192 side opposite is <strong>QR<\/strong><\/p>\n\n\n\n<p>Since <strong>Angle R = 57\u00b0<\/strong> is the smallest, side <strong>PQ<\/strong> is opposite it.<br>So <strong>PQ<\/strong> is the <strong>shortest side<\/strong>.<\/p>\n\n\n\n<p><strong>Corrected answer: A. PQ<\/strong><\/p>\n\n\n\n<p><strong>So the correct answers are:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>C. Angle Y<\/strong><\/li>\n\n\n\n<li><strong>A. PQ<\/strong><\/li>\n<\/ol>\n\n\n\n<p>Apologies for the earlier mistake in the second question \u2014 the correct shortest side is <strong>PQ<\/strong>, not QR.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-692.jpeg\" alt=\"\" class=\"wp-image-35777\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-692.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-692-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-692-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The lengths of sides XY, YZ, and XZ of triangle XYZ are 7 cm, 12 cm, and 15 cm respectively. What angle of the triangle has the largest measure? A. Angle X B. Angle Z C. Angle Y D. Cannot be determined What is the shortest side of triangle PQR if m(P) = 65 and [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-35776","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35776","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=35776"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35776\/revisions"}],"predecessor-version":[{"id":35778,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35776\/revisions\/35778"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=35776"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=35776"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=35776"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}