Question

In the adjoining figure, SR || PQ and ∠PQR = 90°. If PQ = 7 cm, PR = 25 cm and SR = 17 cm, find the length of PS.

Answer 1

Given: PQ || SR

∠PQR = 90°

PQ = 7 cm

PR = 25 cm

SR = 17 cm

Find PS.

Step-wise calculation:

1. Place P at (0, 0) and Q at (7, 0).

So, PQ = 7 along the x-axis and ∠PQR = 90° makes QR vertical.

2. Let R = (7, y).

Use PR = 25:

PR² = (7 – 0)² + (y – 0)² 

⇒ 25² = 7² + y²

y² = 625 – 49

= 576 

⇒ y = 24

So, R = (7, 24).

3. SR || PQ is horizontal and SR = 17.

So, S is 17 units left of R:

S = (7 – 17, 24)

= (–10, 24)

4. Compute PS:

PS² = (–10 – 0)² + (24 – 0)² 

= 100 + 576

= 676

⇒ `PS = sqrt(676)`

⇒ PS = 26 cm