Question

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?
74
52
13
23

Answer 1

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.