{"id":249735,"date":"2025-07-09T19:52:02","date_gmt":"2025-07-09T19:52:02","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=249735"},"modified":"2025-07-09T19:52:04","modified_gmt":"2025-07-09T19:52:04","slug":"which-expresses-all-possible-lengths-of-side-qs","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/09\/which-expresses-all-possible-lengths-of-side-qs\/","title":{"rendered":"Which expresses all possible lengths of side QS"},"content":{"rendered":"\n<p>In triangle QRS, QR = 8 and RS = 5. Which expresses all possible lengths of side QS? O QS = 13 O 5 &lt; QS &lt; 8 O QS > 13 O 3 &lt; QS &lt; 13<\/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>The correct answer is: <strong>3 &lt; QS &lt; 13<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>In any triangle, the lengths of the sides must satisfy the <strong>triangle inequality theorem<\/strong>. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. For triangle QRS, with sides QR = 8, RS = 5, and QS being the unknown side, we can apply the triangle inequality in the following way:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>QR + RS > QS<\/strong><br>This translates to:<br>8 + 5 > QS<br>So,<br>QS &lt; 13<\/li>\n\n\n\n<li><strong>QR + QS > RS<\/strong><br>This translates to:<br>8 + QS > 5<br>So,<br>QS > -3 (which is always true because a side length cannot be negative).<\/li>\n\n\n\n<li><strong>RS + QS > QR<\/strong><br>This translates to:<br>5 + QS > 8<br>So,<br>QS > 3<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Combining these inequalities:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>From the first inequality, we have <strong>QS &lt; 13<\/strong>.<\/li>\n\n\n\n<li>From the third inequality, we have <strong>QS > 3<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the possible lengths of side QS must be between 3 and 13, exclusively. This gives us the final range for QS: <strong>3 &lt; QS &lt; 13<\/strong>.<\/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-banner6-42.jpeg\" alt=\"\" class=\"wp-image-249736\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>In triangle QRS, QR = 8 and RS = 5. Which expresses all possible lengths of side QS? O QS = 13 O 5 &lt; QS &lt; 8 O QS > 13 O 3 &lt; QS &lt; 13 The Correct Answer and Explanation is: The correct answer is: 3 &lt; QS &lt; 13 Explanation: In [&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-249735","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249735","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=249735"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249735\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=249735"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=249735"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=249735"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}