{"id":21373,"date":"2019-05-21T02:54:05","date_gmt":"2019-05-20T21:24:05","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=21373"},"modified":"2022-11-16T21:39:20","modified_gmt":"2022-11-16T16:09:20","slug":"in-the-racetrack-shown-above-regions-i-and-iii-are-semi-circular-with-radius-r-if-region-ii-is-rectangular-and-its-length-is-twice-its-width-what-is-the-perimeter-of-the-track-in-terms-of-r-ogqr","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/in-the-racetrack-shown-above-regions-i-and-iii-are-semi-circular-with-radius-r-if-region-ii-is-rectangular-and-its-length-is-twice-its-width-what-is-the-perimeter-of-the-track-in-terms-of-r-ogqr\/","title":{"rendered":"In the racetrack shown above, regions I and III are semi-circular with radius r. If region II is rectangular and its length is twice its width, what is the perimeter of the track in terms of r? &#8211; OGQR 2020 Question #94 with Solution"},"content":{"rendered":"<span class=\"rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">A <\/span> <span class=\"rt-time\">&lt; 1<\/span> <span class=\"rt-label rt-postfix\">min read <\/span><\/span><h2>OGQR 2020: Question No. 94<\/h2>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-21377 aligncenter\" src=\"https:\/\/e-gmat.com\/blogs\/wp-content\/uploads\/2019\/05\/94.png\" alt=\"\" width=\"280\" height=\"101\"><\/p>\n<p>In the racetrack shown above, regions I and III are semi-circular with radius r. If region II is rectangular and its length is twice its width, what is the perimeter of the track in terms of r?<\/p>\n<table>\n<tbody>\n<tr>\n<td width=\"301\">Source<\/td>\n<td width=\"301\">OGQR 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\">Circle \/ Rectangle<\/td>\n<\/tr>\n<tr>\n<td width=\"301\">Difficulty<\/td>\n<td width=\"301\">Medium<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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 a racetrack consists of two semi-circular regions, with radius r, and one rectangular region.<\/li>\n<li>The length of the rectangular region is twice its width.<\/li>\n<\/ul>\n<h4><strong><u>To Find<\/u><\/strong><\/h4>\n<p>We need to determine<\/p>\n<ul>\n<li>The perimeter of the track, expressed in terms of r.<\/li>\n<\/ul>\n<h4><strong><u>Approach &amp; Working<\/u><\/strong><\/h4>\n<p>The perimeter of each semi-circular region = \u03c0r<\/p>\n<ul>\n<li>Therefore, the perimeter of both semi-circular regions together = 2\u03c0r<\/li>\n<\/ul>\n<p>The rectangular region has length twice its width.<\/p>\n<ul>\n<li>Width of the rectangular region = diameter of the semi-circular region = 2r<\/li>\n<li>Hence, length of the rectangular region = 2 * 2r = 4r<\/li>\n<\/ul>\n<p>Therefore, the perimeter of the whole region = 2\u03c0r + 4r + 4r = 2\u03c0r + 8r = 2r (\u03c0 + 4)<\/p>\n<p>Hence, the correct answer is option B.<\/p>\n<blockquote><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=\"noopener noreferrer 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=\"noopener noreferrer external\" data-wpel-link=\"external\">most reviewed online GMAT Preparation company in GMATClub<\/a><\/strong> with more than 1970 reviews as of December 2020.<\/p><\/blockquote>\n\n<div class=\"ub-buttons align-button-center\"  id=\"ub-button-f5f8907c-d977-4bc1-b7e6-2acd105f4fac\"><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>","protected":false},"excerpt":{"rendered":"<p>OGQR 2020: Question No. 94 In the racetrack shown above, regions I and III are semi-circular with radius r. If region II is rectangular and its length is twice its width, what is the perimeter of the track in terms of r? Source OGQR 2020 Type Problem Solving Topic Geometry Sub-Topic Circle \/ Rectangle Difficulty [&hellip;]<\/p>\n","protected":false},"author":102413,"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":[104,44,94,60,100],"tags":[],"featured_image_src":null,"author_info":{"display_name":"Ashutosh","author_link":"https:\/\/e-gmat.com\/blogs\/author\/ashutoshe-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 the racetrack shown above, regions I and III are semi-circular with radius r. If region II is rectangular and its length is twice its width, what is the perimeter of the track in terms of r? - OGQR 2020 Question #94 with Solution<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/e-gmat.com\/blogs\/in-the-racetrack-shown-above-regions-i-and-iii-are-semi-circular-with-radius-r-if-region-ii-is-rectangular-and-its-length-is-twice-its-width-what-is-the-perimeter-of-the-track-in-terms-of-r-ogqr\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"In the racetrack shown above, regions I and III are semi-circular with radius r. 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