{"id":154942,"date":"2024-10-15T16:27:38","date_gmt":"2024-10-15T16:27:38","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=154942"},"modified":"2024-10-15T16:28:12","modified_gmt":"2024-10-15T16:28:12","slug":"in-triangle-scu-shown-below-points-t-and-o-are-on-su-and-cu-respectively-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/15\/in-triangle-scu-shown-below-points-t-and-o-are-on-su-and-cu-respectively-2\/","title":{"rendered":"In triangle SCU shown below"},"content":{"rendered":"\n<p>In triangle SCU shown below, points T and O are on SU and CU respectively. Segment OT is drawn so that angle C is congruent to angle OTU. If TU=4, OU=5, and OC=7,what is the length of ST<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To solve for the length of segment ( ST ) in triangle ( SCU ) with points ( T ) and ( O ) on segments ( SU ) and ( CU ), respectively, we can utilize properties of similar triangles and the concept of angle congruence.<\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( TU = 4 )<\/li>\n\n\n\n<li>( OU = 5 )<\/li>\n\n\n\n<li>( OC = 7 )<\/li>\n<\/ul>\n\n\n\n<p>Since ( \\angle C \\cong \\angle OTU ), triangles ( OCU ) and ( OTU ) are similar by the AA (Angle-Angle) similarity criterion. This means that the corresponding sides of these triangles are proportional.<\/p>\n\n\n\n<p>Let&#8217;s denote:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( ST = x )<\/li>\n\n\n\n<li>( SU = ST + TU = x + 4 )<\/li>\n\n\n\n<li>( CU = OC + OU = 7 + 5 = 12 )<\/li>\n<\/ul>\n\n\n\n<p>Using the property of similar triangles, we can set up the following proportion based on the corresponding sides:<\/p>\n\n\n\n<p>[<br>\\frac{ST}{TU} = \\frac{OC}{OU}<br>]<\/p>\n\n\n\n<p>Substituting the known values into the proportion:<\/p>\n\n\n\n<p>[<br>\\frac{x}{4} = \\frac{7}{5}<br>]<\/p>\n\n\n\n<p>Now, we can cross-multiply to solve for ( x ):<\/p>\n\n\n\n<p>[<br>5x = 4 \\cdot 7<br>]<br>[<br>5x = 28<br>]<br>[<br>x = \\frac{28}{5}<br>]<br>[<br>x = 5.6<br>]<\/p>\n\n\n\n<p>Thus, the length of segment ( ST ) is ( 5.6 ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Triangle Similarity<\/strong>: The key to solving this problem is recognizing the similarity between triangles ( OCU ) and ( OTU ). Since ( \\angle C ) is congruent to ( \\angle OTU ), and both triangles share angle ( U ), we can confidently apply the properties of similar triangles.<\/li>\n\n\n\n<li><strong>Setting Up Proportions<\/strong>: By defining the lengths of segments in terms of ( ST ) and using known values for the other segments, we can express the relationship between the sides of the triangles through a proportion.<\/li>\n\n\n\n<li><strong>Solving the Equation<\/strong>: After establishing the proportion, it is a matter of algebraic manipulation to find ( x ), which represents the length of ( ST ).<\/li>\n<\/ol>\n\n\n\n<p>In conclusion, the calculated length of ( ST ) is ( 5.6 ), determined through the application of triangle similarity and proportional reasoning.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In triangle SCU shown below, points T and O are on SU and CU respectively. Segment OT is drawn so that angle C is congruent to angle OTU. If TU=4, OU=5, and OC=7,what is the length of ST The Correct Answer and Explanation is : To solve for the length of segment ( ST ) [&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-154942","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/154942","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=154942"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/154942\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=154942"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=154942"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=154942"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}