Question

In ΔPQR, PS ⊥ QR, PR = 41 cm, SR = 9 cm, QS = 30 cm.

The value of y is ______.

Options

• 50 cm

• 55 cm

• 60 cm

• 45 cm

Answer 1

The value of y is 50 cm.

Explanation:

Given, PS ⊥ QR, PR = 41 cm, SR = 9 cm, QS = 30 cm.

First, find x = PS using right triangle PRS:

PR² = PS² + SR² 

41² = x² + 9² 

1681 = x² + 81 

x² = 1681 – 81

x² = 1600

x = `sqrt(1600)`

x = 40 cm

Now use right triangle PQ to find y:

PQ² = PS² + QS²

y² = 40² + 30²

y² = 1600 + 900

y² = 2500

y = `sqrt(2500)`

y = 50 cm