Question

In the given figure, PQ = 24 cm, PR = 25 cm, ∠PQR = 90°, find the radius of inscribed circle of ΔPQR.

Answer 1

Given

PQ = 24 cm

PR = 25 cm

∠PQR = 90°

Triangle PQR is right-angled at Q.

Radius of the incircle of ΔPQR.

Step 1: Find QR (the third side)

Using Pythagoras theorem:

PR² = PQ² + QR²

25² = 24² + QR²

625 = 576 + QR²

QR² = 49

QR = 7 cm

Step 2: Use the incircle radius formula for a right triangle.

For a right-angled triangle with legs a, b, and hypotenuse c:

r = `(a + b − c)/2`

Here,

a = PQ = 24 cm

b = QR = 7 cm

c = PR = 25 cm

r = `(24 + 7 − 25)/2`     ...[Substitute]

r = `6/2`

r = 3 cm