Question

In ΔABC, AD ⊥ BC. AB = 10 cm, BD = 6 cm, DC = 15 cm.

The value of y is ______.

Options

• 20 cm

• 25 cm

• 17 cm

• 13 cm

Answer 1

The value of y is 17 cm.

Explanation:

In ΔABC, AD ⊥ BC. AB = 10 cm, BD = 6 cm, DC = 15 cm.

In ΔABD,

By Pythagoras theorem,

AB² = AD² + BD²

10² = x² + 6²

100 = x² + 36

x² = 64

⇒ x = 8

In ΔADC,

Again using Pythagoras theorem,

AC² = AD² + DC²

AC² = 8² + 15²

AC² = 64 + 225

AC² = 289

AC = `sqrt(289)`

AC = 17 cm