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CAT Geometry Solutions

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  • Rajesh Balasubramanian
    Hi all, Have given below the solutions to the questions on geometry. These can also be found at our blog at
    Message 1 of 1 , Aug 26, 2011
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      Hi all,
       
      Have given below the solutions to the questions on geometry. These can also be found at our blog at http://iimcat.blogspot.com/2011/08/cat-geometry-solutions.html 

      1. Perimeter of a triangle with integer sides is equal to 15. How many such triangles are possible?

      This is just a counting question, with the caveat that sum of two sides should be greater than the third. Let us assume a < b < c

      a = 1, Possible triangle 1, 7, 7
      a = 2, possible triangle 2, 6, 7
      a = 3, possible triangles 3, 6, 6 and 3, 5, 7
      a = 4, possible triangles 4, 4, 7 and 4, 5, 6

      There are totally 6 triangles possible

      2. Triangle ABC has integer sides x, y, z such that xz = 12. How many such triangles are possible?

      xz = 12

      x,z can be 1, 12 or 2, 6 or 3, 4

      Possible triangles
      1-12-12
      2-6-5; 2-6-6; 2-6-7
      3-4-2; 3-4-3; 3-4-5; 3-4-6

      8 triangles are possible

      3. Triangle has sides a^2, b^2 and c^2. Then the triangle with sides a, b, c has to be - a) Right angled b) Acute-angled c) Obtuse angled d) can be any of these three

      Assuming a < b < c, we have a^2 + b^2 > c^2. This implies the triangle with sides a, b, c has to be acute-angled

      Regards,
      99626 48484
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