Question

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

The value of x is ______.

Options

• 36 cm

• 35 cm

• 40 cm

• 38 cm

Answer 1

The value of x is 40 cm.

Explanation:

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

We need to find x, the perpendicular height PS.

Since PS is perpendicular to QR, triangles PQS and PRS are right triangles.

Using the right triangle PRS:

PR² = PS² + SR² 

41² = x² + 9² 

1681 = x² + 81 

x² = 1681 – 81

x² = 1600

x = `sqrt(1600)`

x = 40 cm