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CAT 2021 Exam Question Papers Slot 1 | CAT Quants

CAT Quantitative Aptitude | CAT 2021 Question Papers

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All CAT 2021 Quantitative aptitude questions have detailed answer keys and solutions provided by our experts. Watch the videos below to learn the fastest ways to answer the questions:

6).

Suppose the length of each side of a regular hexagon ABCDEF is 2 cm . If T is the mid point of CD, then the length of AT in cm is

  1. √15 cm

  2. √13 cm

  3. √12 cm

  4. √14 cm


Explanation

In hexagon, ABCDEF, angleABC = 120o , and in triangle ABC, angle ACB = 30o

        

 

So, in triangle ACT, angleACT = 90o   

         In right angle triangle ACT, CT = 1 cm. If we find out AC, AT can be determined.

         To find AC, drop perpendicular G on AC.

         In right angle triangle AGB, AG = AB sin 60o =  2 x (fraction numerator square root of 3 over denominator 2 end fraction) = square root of 3

         So, AC = 2square root of 3 cm

         Now , in increment ACT, applying Pythagoras theorem,

                AT2 = AC2 + CT= (2square root of 3)2 + 1= 13

  • AT = square root of 13   cm

Ans: square root of 13

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