Question

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

Answer 1

Given,

ΔDCB is right angle triangle, right angle at C.

Here base (BC) = 12

Hypotenuse (DB) = x = ?

Perpendicular (DC) = 12

To find DB, apply Pythagoras theorem in ΔDCB.

(DB)² = (DC)² + (BC)²

(x)² = (9)² + (12)²

x² = 81 + 144

x = `sqrt(225)`

x = 15

Thus, DB = x = 15

Now, ∆ADB is right angle triangle, right angle at S.

Here base (DB) = 15

Hypotenuse (AB) = y = ?

Perpendicular (AD) = 8

Apply Pythagoras theorem in ∆ADQ.

(AB)² = (AD)² + (DB)²

y² = (8)² + (15)²

y² = 64 + 225

y = `sqrt(289)`

y = 17

Thus, AB = y = 17

Hence, x = 15, y = 17.