In ΔPQR, m∠Q : m∠R : m∠P = 1 : 2 : 1. If PQ = 2√6, find PR.

Given: Ratio of angles of triangles =  mQ : mR : mP = 1 : 2 : 1

Let mQ = x, mR = 2 x, mP = x

Sum of angles of triangle = 180°

mQ + mR + mP = 180°

⇒  x + 2x + x = 180°

⇒ 4x = 180

⇒ x = 45

So by putting value of x we get,

⇒ mR = 90
⇒ mQ = 45°
⇒ mP = 45°

It is an isosceles right angled triangle at R.

Let PR = QR = d

According to pythagoras theorem, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides

Applying Pythagoras theorem 

PR² + QR² = PQ²

2d² = PQ²

⇒ 2d² = 24

⇒ d² = 12

⇒ d = 2√3

So PR = 2√3 units

and QR = 2√3 units