Question

A triangle PQR is an isosceles triangle right angled at Q . Is PR square = 2PQ square​

Answer 1

This is the required answer

Answer 2

Given : PQR is an isosceles triangle and right angle at Q

To Prove : $(PR)^{2}\: = \: 2(PQ)^{2}$

Solution :

PR is Hypotenuse

Hypotenuse is greater than other two sides of triangle.

So, it's mean PQ = QR ( as triangle is isosceles triangle )

By pythagorean theorem

$(PR)^{2} = (PQ)^{2}\: + \: (QR)^{2}$

$(PR)^{2} = (PQ)^{2}\: + \: (PQ)^{2}$ .. (given)

$(PR)^{2} = 2(PQ)^{2}$

Hence Proved