{"id":21445,"date":"2019-05-21T14:39:24","date_gmt":"2019-05-21T09:09:24","guid":{"rendered":"https:\/\/e-gmat.com\/blogs\/?p=21445"},"modified":"2019-05-21T14:39:24","modified_gmt":"2019-05-21T09:09:24","slug":"if-a-is-the-area-of-a-triangle-with-sides-of-lengths-x-y-and-z-as-shown-above-what-is-the-value-of-a-ogqr-2020-question-220-with-solution","status":"publish","type":"post","link":"https:\/\/e-gmat.com\/blogs\/if-a-is-the-area-of-a-triangle-with-sides-of-lengths-x-y-and-z-as-shown-above-what-is-the-value-of-a-ogqr-2020-question-220-with-solution\/","title":{"rendered":"If\u00a0A\u00a0is the area of a triangle with sides of lengths\u00a0x,\u00a0y, and\u00a0z\u00a0as shown above, what is the value of\u00a0A? – OGQR 2020 Question #220 with Solution"},"content":{"rendered":"A <\/span> 2<\/span> min read <\/span><\/span>
\n\t\t\t\t\t

OGQR 2020: Question No. 220<\/h2>\n

<\/p>\n

If\u00a0A\u00a0is the area of a triangle with sides of lengths\u00a0x,\u00a0y, and\u00a0z\u00a0as shown above, what is the value of\u00a0A?<\/p>\n

    \n
  1. z\u00a0=\u00a013<\/li>\n
  2. A\u00a0= 5y\/2<\/li>\n<\/ol>\n\t\t\t\t<\/div>\n
    \n\t\t\t\t\t\n\n\n\n\n\n\n
    Source<\/td>\nOGQR 2020<\/td>\n<\/tr>\n
    Type<\/td>\nData Sufficiency<\/td>\n<\/tr>\n
    Topic<\/td>\nGeometry<\/td>\n<\/tr>\n
    Sub-Topic<\/td>\nTriangles<\/td>\n<\/tr>\n
    Difficulty<\/td>\nMedium<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\t\t\t\t<\/div>
    <\/div>\n

    Solution<\/h3>\n

    Steps 1 & 2: Understand Question and Draw Inferences<\/u><\/strong><\/h4>\n

    In this question, we are given:<\/p>\n

      \n
    • A right-angle triangle of area A<\/li>\n
    • Side lengths of the triangle are: x, y, and z.<\/li>\n<\/ul>\n

      We need to find:<\/p>\n

        \n
      • The value of A.<\/li>\n<\/ul>\n

        Now, the given triangle is a right-angled triangle.<\/p>\n

          \n
        • Hence, its area A = 1\/2 * xy<\/li>\n<\/ul>\n

          Therefore, if we know the value of x and y or their product, we can find the value of A.<\/p>\n

          With this understanding, let us now analyse the individual statements.<\/p>\n

           <\/p>\n

          Step 3: Analyse Statement 1<\/u><\/strong><\/h4>\n

          \u201cz\u00a0=\u00a013\u201d<\/em><\/p>\n

          Since we do not get the values of x and y from this statement, statement 1 is not sufficient to answer the question.<\/p>\n

           <\/p>\n

          Step 4: Analyse Statement 2<\/u><\/strong><\/h4>\n

          \u201cA\u00a0= 5y\/2<\/em>\u201d<\/em><\/p>\n

            \n
          • 1\/2 * xy = 5y\/2<\/li>\n<\/ul>\n

            Or, x = 5<\/p>\n

            However, we do not know the value of y.<\/p>\n

            Therefore, statement 2 is not sufficient to answer the question.<\/p>\n

             <\/p>\n

            Step 5: Combine Both Statements Together (If Needed)<\/u><\/strong><\/h4>\n

            From statement 1: z =13<\/p>\n

            From statement 2: x = 5<\/p>\n

            On applying Pythagoras theorem in the given triangle, we get: x2<\/sup> + y2<\/sup> = z2<\/sup><\/p>\n

              \n
            • 52<\/sup> + y2<\/sup> = 132<\/sup><\/li>\n<\/ul>\n

              From this equation, we can find y.<\/p>\n

                \n
              • Hence, we can find the value of A.<\/li>\n<\/ul>\n

                Since we could find the answer by combining both the statements, option C is the correct answer.<\/p>\n","protected":false},"excerpt":{"rendered":"

                Solution Steps 1 & 2: Understand Question and Draw Inferences In this question, we are given: A right-angle triangle of area A Side lengths of the triangle are: x, y, and z. We need to find: The value of A. Now, the given triangle is a right-angled triangle. Hence, its area A = 1\/2 * […]<\/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":"","footnotes":""},"categories":[104,44,94,60,100],"tags":[],"class_list":["post-21445","post","type-post","status-publish","format-standard","hentry","category-geometry","category-gmat-official-guide-solutions","category-gmat-prep","category-gmat-quant","category-quant-official-guide-solutions","et-doesnt-have-format-content","et_post_format-et-post-format-standard"],"featured_image_src":null,"author_info":{"display_name":"Juhi Gupta","author_link":"https:\/\/e-gmat.com\/blogs\/author\/juhie-gmat-com\/"},"yoast_head":"\nIf\u00a0A\u00a0is the area of a triangle with sides of lengths\u00a0x,\u00a0y, and\u00a0z\u00a0as shown above, what is the value of\u00a0A? - OGQR 2020 Question #220 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\/if-a-is-the-area-of-a-triangle-with-sides-of-lengths-x-y-and-z-as-shown-above-what-is-the-value-of-a-ogqr-2020-question-220-with-solution\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If\u00a0A\u00a0is the area of a triangle with sides of lengths\u00a0x,\u00a0y, and\u00a0z\u00a0as shown above, what is the value of\u00a0A? - OGQR 2020 Question #220 with Solution\" \/>\n<meta property=\"og:description\" content=\"Solution Steps 1 & 2: Understand Question and Draw Inferences In this question, we are given: A right-angle triangle of area A Side lengths of the triangle are: x, y, and z. 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