{"id":249731,"date":"2025-07-09T19:49:13","date_gmt":"2025-07-09T19:49:13","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=249731"},"modified":"2025-07-09T19:49:16","modified_gmt":"2025-07-09T19:49:16","slug":"which-expresses-all-possible-length-of-side-qs","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/09\/which-expresses-all-possible-length-of-side-qs\/","title":{"rendered":"Which expresses all possible length of side QS"},"content":{"rendered":"\n<p>In triangle QRS, QR = 8 and RS = 5. Which expresses all possible length of side QS? A) QS = 13 B) 5 &lt; QS &lt; 8 C) QS > 13 D) 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>To determine the possible lengths of side QS in triangle QRS, we apply the <strong>triangle inequality theorem<\/strong>. The triangle inequality 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.<\/p>\n\n\n\n<p>We know that:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>QR = 8<\/li>\n\n\n\n<li>RS = 5<\/li>\n\n\n\n<li>QS is the unknown side.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Applying the triangle inequality theorem:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>QR + RS > QS<\/strong><br>This inequality implies:<br>8+5>QS8 + 5 > QS8+5>QS<br>13>QS13 > QS13>QS<br>Hence, QS must be less than 13.<\/li>\n\n\n\n<li><strong>QR + QS > RS<\/strong><br>This inequality implies:<br>8+QS>58 + QS > 58+QS>5<br>QS>5\u22128QS > 5 &#8211; 8QS>5\u22128<br>QS>\u22123QS > -3QS>\u22123<br>Since the length of a side must always be positive, we can disregard the negative result. Therefore, this inequality does not provide new information.<\/li>\n\n\n\n<li><strong>RS + QS > QR<\/strong><br>This inequality implies:<br>5+QS>85 + QS > 85+QS>8<br>QS>8\u22125QS > 8 &#8211; 5QS>8\u22125<br>QS>3QS > 3QS>3<br>Hence, QS must be greater than 3.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Combining the results:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>From the first inequality, we have QS&lt;13QS &lt; 13QS&lt;13.<\/li>\n\n\n\n<li>From the second inequality, we have QS>3QS > 3QS>3.<\/li>\n<\/ul>\n\n\n\n<p>Thus, the possible length of QS lies between 3 and 13, so we have:<br><strong>3 &lt; QS &lt; 13<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Correct Answer:<\/h3>\n\n\n\n<p><strong>D) 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-banner6-41.jpeg\" alt=\"\" class=\"wp-image-249732\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>In triangle QRS, QR = 8 and RS = 5. Which expresses all possible length of side QS? A) QS = 13 B) 5 &lt; QS &lt; 8 C) QS > 13 D) 3 &lt; QS &lt; 13 The Correct Answer and Explanation is: To determine the possible lengths of side QS in triangle QRS, [&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-249731","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249731","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=249731"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249731\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=249731"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=249731"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=249731"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}