Question

In the following figure, find the sides marked x and y.

Answer 1

Given,

ΔPQR is right angle triangle, right angle at Q.

Here base (QR) = 16

Hypotenuse (PR) = 20

Perpendicular (PQ) = x = ?

To find PQ, apply Pythagoras theorem in ΔPQR.

(PR)² = (PQ)² + (QR)²

(20)² = (x)² + (16)²

x² = 400 – 256

x = `sqrt(144)`

x = 12

Thus, PQ = x = 12

Now, ∆SPR is right angle triangle, right angle at P.

Here base (PR) = 20

Hypotenuse (SR) = 29

Perpendicular (SP) = y = ?

Apply Pythagoras theorem in ∆SPR.

(SR)² = (SP)² + (PR)²

(29)² = (y)² + (20)²

y² = 29² – 20²

y² = 841 – 400

y = `sqrt(441)`

y = 21

Thus, SP = y = 21

Hence, x = 12, y = 21.