Question

In quadrilateral PQRS, ∠Q = 90° = ∠S, SP = 15 cm, PQ = 7 cm, QR = 24 cm.

The length of SR is ______.

Options

• 18 cm

• 20 cm

• 16 cm

• 24 cm

Answer 1

The length of SR is 20 cm.

Explanation:

In △PQR,

By Pythagoras theorem,

PR² = PQ² + QR²

= 7² + 24²

= 49 + 576

= 625

PR = `sqrt(625)`

= 25 cm

In △PSR,

By Pythagoras theorem,

PR² = SP² + SR²

⇒ 25² = 15² + SR²

⇒ 625 = 225 + SR²

⇒ SR² = 625 – 225

⇒ SR² = 400

⇒ SR = `sqrt(400)`

⇒ SR = 20 cm