Question

In the adjoining figure, ∠RQS = 90°, ∠QPS = 90°, RS = 25 cm, QR = 20 cm, PQ = 9 cm. Find PS.

Answer 1

Given: In the figure

∠RQS = 90°

∠QPS = 90°

RS = 25 cm

QR = 20 cm

PQ = 9 cm

Step-wise calculation:

1. In right triangle RQS right angle at Q.

By Pythagoras: 

QS² + QR² 

= RS² – QS²

= 25² – 20²

= 625 – 400

= 225

⇒ QS = 15 cm

2. In right triangle PQS right angle at P.

By Pythagoras: 

PQ² + PS²

= QS² – PS²

= QS² – PQ²

= 15² – 9²

= 225 – 81

= 144

⇒ PS = 12 cm