Q. 105.0( 1 Vote )

# In ΔPQR, m∠

Answer :

Given: Ratio of angles of triangles =  m Q : m R : m P = 1 : 2 : 1

Let m Q = x, m R = 2 x, m P = x

Sum of angles of triangle = 180°

m Q + m R + m P = 180°

⇒  x + 2x + x = 180°

⇒ 4x = 180

⇒ x = 45

So by putting value of x we get,

⇒ m R = 90
⇒ m Q = 45°
⇒ m P = 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

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