{"id":170727,"date":"2024-11-19T22:42:22","date_gmt":"2024-11-19T22:42:22","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=170727"},"modified":"2024-11-19T22:42:24","modified_gmt":"2024-11-19T22:42:24","slug":"what-value-of-x-will-make-parallelogram-abcd-a-rhombus","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/19\/what-value-of-x-will-make-parallelogram-abcd-a-rhombus\/","title":{"rendered":"What value of x will make parallelogram ABCD a rhombus"},"content":{"rendered":"\n<p>What value of x will make parallelogram ABCD a rhombus?<\/p>\n\n\n\n<p>x =<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2024\/11\/image-19.png\" alt=\"\" class=\"wp-image-170728\"\/><\/figure>\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 determine the value of ( x ) that will make parallelogram ABCD a rhombus, we need to use the defining property of a rhombus: <strong>all four sides of a rhombus are congruent<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Problem Analysis<\/h3>\n\n\n\n<p>From the image:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Parallelogram ABCD has sides labeled with algebraic expressions:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>One pair of opposite sides is ( 2x + 3 ) and the other is ( 3x &#8211; 4 ).<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li>To make ABCD a rhombus, the side lengths must all be equal:<br>[<br>2x + 3 = 3x &#8211; 4<br>]<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Solving the Equation<\/h3>\n\n\n\n<p>Step 1: Set the side expressions equal to each other:<br>[<br>2x + 3 = 3x &#8211; 4<br>]<\/p>\n\n\n\n<p>Step 2: Subtract ( 2x ) from both sides to isolate ( x ) terms on one side:<br>[<br>3 = x &#8211; 4<br>]<\/p>\n\n\n\n<p>Step 3: Add ( 4 ) to both sides to solve for ( x ):<br>[<br>x = 7<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Verification<\/h3>\n\n\n\n<p>If ( x = 7 ):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The length of one side is:<br>[<br>2x + 3 = 2(7) + 3 = 14 + 3 = 17<br>]<\/li>\n\n\n\n<li>The length of the other side is:<br>[<br>3x &#8211; 4 = 3(7) &#8211; 4 = 21 &#8211; 4 = 17<br>]<br>Since both sides are equal, all four sides of the parallelogram will be 17, confirming it is a rhombus.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>A parallelogram becomes a rhombus when all its sides are of equal length. By setting the expressions for adjacent sides equal, we solved for ( x ) and verified that it satisfies the condition of a rhombus. This method uses basic algebra and the geometric property of a rhombus, ensuring logical and accurate results.<\/p>\n\n\n\n<p>Thus, the correct value of ( x ) is:<br>[<br>\\boxed{7}<br>]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What value of x will make parallelogram ABCD a rhombus? x = The Correct Answer and Explanation is : To determine the value of ( x ) that will make parallelogram ABCD a rhombus, we need to use the defining property of a rhombus: all four sides of a rhombus are congruent. Problem Analysis From [&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-170727","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/170727","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=170727"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/170727\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=170727"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=170727"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=170727"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}