{"id":266726,"date":"2025-07-23T06:43:03","date_gmt":"2025-07-23T06:43:03","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=266726"},"modified":"2025-07-23T06:43:05","modified_gmt":"2025-07-23T06:43:05","slug":"helppp-if-on-8x-8-lm-7x-4-nm-x-5-and-ol-3y-6-find-the-values-of-x-and-y-for-which-lmno-must-be-a-parallelogram","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/23\/helppp-if-on-8x-8-lm-7x-4-nm-x-5-and-ol-3y-6-find-the-values-of-x-and-y-for-which-lmno-must-be-a-parallelogram\/","title":{"rendered":"HELPPP!! If ON = 8x &#8211; 8, LM = 7x + 4, NM = x &#8211; 5, and OL = 3y &#8211; 6, find the values of x and y for which LMNO must be a parallelogram."},"content":{"rendered":"\n<p>HELPPP!! If ON = 8x &#8211; 8, LM = 7x + 4, NM = x &#8211; 5, and OL = 3y &#8211; 6, find the values of x and y for which LMNO must be a parallelogram.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>For LMNO to be a parallelogram, opposite sides must be equal in length. The opposite sides of the parallelogram in this case are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>LM<\/strong> and <strong>ON<\/strong><\/li>\n\n\n\n<li><strong>NM<\/strong> and <strong>OL<\/strong><\/li>\n<\/ul>\n\n\n\n<p>So, we can equate the expressions for these pairs of opposite sides to find the values of xxx and yyy.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Equate opposite sides<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>LM = ON<\/strong><br>From the given information, 7x+4=8x\u221287x + 4 = 8x &#8211; 87x+4=8x\u22128 Now, solve for xxx: 7x+4=8x\u221287x + 4 = 8x &#8211; 87x+4=8x\u22128 Subtract 7x7x7x from both sides: 4=x\u221284 = x &#8211; 84=x\u22128 Add 8 to both sides: x=12x = 12x=12<\/li>\n\n\n\n<li><strong>NM = OL<\/strong><br>From the given information, x\u22125=3y\u22126x &#8211; 5 = 3y &#8211; 6x\u22125=3y\u22126 Substitute x=12x = 12x=12 into this equation: 12\u22125=3y\u2212612 &#8211; 5 = 3y &#8211; 612\u22125=3y\u22126 Simplify: 7=3y\u221267 = 3y &#8211; 67=3y\u22126 Add 6 to both sides: 13=3y13 = 3y13=3y Divide both sides by 3: y=133y = \\frac{13}{3}y=313\u200b<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>The values of xxx and yyy are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>x=12x = 12x=12<\/li>\n\n\n\n<li>y=133y = \\frac{13}{3}y=313\u200b<\/li>\n<\/ul>\n\n\n\n<p>Thus, for LMNO to be a parallelogram, xxx must be 12 and yyy must be 133\\frac{13}{3}313\u200b.<\/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-banner6-1608.jpeg\" alt=\"\" class=\"wp-image-266731\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>HELPPP!! If ON = 8x &#8211; 8, LM = 7x + 4, NM = x &#8211; 5, and OL = 3y &#8211; 6, find the values of x and y for which LMNO must be a parallelogram. The Correct Answer and Explanation is: For LMNO to be a parallelogram, opposite sides must be equal 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-266726","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/266726","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=266726"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/266726\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=266726"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=266726"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=266726"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}