CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Trigonometry

The question is from CAT Geometry - Trigonometry. This is about Right Triangle. Our task is to identify the value of the hypotenuse which is not possible with the given conditions. Trigonometry is an important topic for CAT Preparation for the CAT Exam. Trigonometric ideas can be completely opposite, as in, some questions test lot of common sense with direction, heights and distances, while others could test you on identities. CAT exam could test one on both these fronts. Make sure you master both in CAT - Trigonometry.

Question 10: A right angled triangle has a height ‘p’, base ‘b’ and hypotenuse ‘h’. Which of the following value can h² not take, given that p and b are positive integers?

1. 74
2. 52
3. 13
4. 23

Explanatory Answer

Method of solving this CAT Question from CAT Geometry - Trigonometry : Can we try trial and error?

We know that,
h² = p² + b² Given, p and b are positive integer, so h² will be sum of two perfect squares.

We see
a) 7² + 5² = 74
b) 6² + 4² = 52
c) 3² + 2² = 13
d) Can’t be expressed as a sum of two perfect squares

The question is "Which of the following value can h² not take, given that p and b are positive integers? "

Hence, the answer is 23

Choice D is the correct answer.