{"id":21464,"date":"2019-05-21T19:43:39","date_gmt":"2019-05-21T14:13:39","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=21464"},"modified":"2022-11-16T21:18:56","modified_gmt":"2022-11-16T15:48:56","slug":"in-quadrilateral-abcd-above-what-is-the-length-of-ab-og-2020-question-97-with-solution","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/in-quadrilateral-abcd-above-what-is-the-length-of-ab-og-2020-question-97-with-solution\/","title":{"rendered":"In quadrilateral ABCD above, what is the length of AB? &#8211; OG 2020 Question #97 with Solution"},"content":{"rendered":"<span class=\"rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">A <\/span> <span class=\"rt-time\">2<\/span> <span class=\"rt-label rt-postfix\">min read <\/span><\/span><div class='two_third'>\n\t\t\t\t\t<h2>OG 2020: Question No. 97<\/h2>\n<p><img class=\"aligncenter\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/05\/OG_PS_97_1.png\" \/><\/p>\n<p>In quadrilateral ABCD above, what is the length of AB?<\/p>\n<ol>\n<li>\u221a26<\/li>\n<li>2\u221a5<\/li>\n<li>2\u221a6<\/li>\n<li>3\u221a2<\/li>\n<li>3\u221a3<\/li>\n<\/ol>\n\t\t\t\t<\/div>\n<div class='one_third et_column_last'>\n\t\t\t\t\t<table>\n<tbody>\n<tr>\n<td width=\"301\">Source<\/td>\n<td width=\"301\">OG 2020<\/td>\n<\/tr>\n<tr>\n<td width=\"301\">Type<\/td>\n<td width=\"301\">Problem Solving<\/td>\n<\/tr>\n<tr>\n<td width=\"301\">Topic<\/td>\n<td width=\"301\">Geometry<\/td>\n<\/tr>\n<tr>\n<td width=\"301\">Sub-Topic<\/td>\n<td width=\"301\">Triangle<\/td>\n<\/tr>\n<tr>\n<td width=\"301\">Difficulty<\/td>\n<td width=\"301\">Medium<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\t\t\t\t<\/div><div class='clear'><\/div>\n<h3>Solution<\/h3>\n<h4><strong><u>Given<\/u><\/strong><\/h4>\n<p>In this question, we are given<\/p>\n<ul>\n<li>The diagram of the quadrilateral ABCD<\/li>\n<li>Length of AD = 1, DC = 3 and CB = 4<\/li>\n<li>Angle BAD = angle DCB = 90\u00b0<\/li>\n<\/ul>\n<p>\u00a0<\/p>\n<h4><strong><u>To Find<\/u><\/strong><\/h4>\n<p>We need to determine<\/p>\n<ul>\n<li>The length of AB<\/li>\n<\/ul>\n<p>\u00a0<\/p>\n<h4><strong><u>Approach &amp; Working<\/u><\/strong><\/h4>\n<p>In the given figure, if we add the points B and D, we get two right-angle triangles ABD and CBD.<\/p>\n<p><img class=\"aligncenter\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/05\/OG_PS_97_2.png\" \/><\/p>\n<p>Now, in triangle BCD, angle BCD = 90\u00b0<\/p>\n<ul>\n<li>Therefore, BD<sup>2<\/sup> = BC<sup>2<\/sup> + CD<sup>2<\/sup> = 4<sup>2<\/sup> + 3<sup>2<\/sup> = 16 + 9 = 25 = 5<sup>2<\/sup><\/li>\n<li>Hence, BD = 5<\/li>\n<\/ul>\n<p>Similarly, in triangle BAD, angle BAD = 90\u00b0<\/p>\n<ul>\n<li>Hence, BD<sup>2<\/sup> = BA<sup>2<\/sup> + AD<sup>2<\/sup><\/li>\n<\/ul>\n<p>Or, BA<sup>2<\/sup> = BD<sup>2<\/sup> \u2013 AD<sup>2<\/sup> = 5<sup>2<\/sup> \u2013 1<sup>2<\/sup> = 25 \u2013 1 = 24 = 4 * 6<\/p>\n<ul>\n<li>Therefore, BA = \u221a(4 * 6) = 2\u221a6<\/li>\n<\/ul>\n<p>Hence, the correct answer is option C.<\/p>\n<p>\u00a0<\/p>\n\n\n<blockquote class=\"wp-block-quote\"><p>Did you know a 700+ GMAT Score can increase your chances to get into your dream business school? We can help you achieve that. Why don\u2019t you<a href=\"https:\/\/e-gmat.com\/ft-gmat\/?channel=blogsin_article&amp;utm_source=blogs&amp;utm_medium=in_article&amp;utm_campaign=free_trial&amp;utm_term=blogs_in_article_lekhika\" target=\"_blank\" rel=\"noreferrer noopener external\" data-wpel-link=\"external\">&nbsp;<strong>try out our FREE Trial?<\/strong><\/a><strong>&nbsp;<\/strong>We are the<strong>&nbsp;<a href=\"https:\/\/gmatclub.com\/reviews\/e-gmat-6\" target=\"_blank\" rel=\"noreferrer noopener external\" data-wpel-link=\"external\">most reviewed online GMAT Preparation company in GMATClub<\/a><\/strong>&nbsp;with more than 1950 reviews as of October 2020.<\/p><\/blockquote>\n\n\n<div class=\"ub-buttons align-button-center\"  id=\"ub-button-21999d31-eb77-4d11-a0d5-0b759f26177f\"><div class=\"ub-button-container\">\n    <a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" target=\"_blank\" rel=\"noopener noreferrer external\" class=\"ub-button-block-main ub-button-medium ub-button-flex-medium\" role=\"button\" data-wpel-link=\"external\">\n    <div class=\"ub-button-content-holder\"><span class=\"ub-button-block-btn\">Sign up for a Free Trial<\/span>\n    <\/div><\/a><\/div><\/div>\n\n\n<p><a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" target=\"_blank\" rel=\"noreferrer noopener external\" data-wpel-link=\"external\"><\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/resources.e-gmat.com\/sign-up-free-trial\" target=\"_blank\" rel=\"noreferrer noopener external\" data-wpel-link=\"external\"><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution Given In this question, we are given The diagram of the quadrilateral ABCD Length of AD = 1, DC = 3 and CB = 4 Angle BAD = angle DCB = 90\u00b0 \u00a0 To Find We need to determine The length of AB \u00a0 Approach &amp; Working In the given figure, if we add [&hellip;]<\/p>\n","protected":false},"author":79663,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","ub_ctt_via":""},"categories":[44,94,100],"tags":[],"featured_image_src":null,"author_info":{"display_name":"Juhi Gupta","author_link":"https:\/\/e-gmat.com\/blogs\/author\/juhie-gmat-com\/"},"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.1.1 (Yoast SEO v17.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>In quadrilateral ABCD above, what is the length of AB? 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