Question

In ΔABC, AD ⊥ BC, AB = 13 cm, AC = 15 cm, AD = 12 cm.

∴ BC is ______.

Options

• `sqrt(394)`

• 9 cm

• 14 cm

• 15 cm

Answer 1

BC is 14 cm.

Explanation:

In ΔABC, AD ⊥ BC, AB = 13 cm, AC = 15 cm, AD = 12 cm.

Apply Pythagoras theorem in ΔABC,

AB² = AD² + BD²

⇒ 13² = 12² + BD²

⇒ 169 = 144 + BD²

⇒ BD² = 25

⇒ BD = 5 cm

Again Apply Pythagoras theorem in ΔACD,

AC² = AD² + CD²

⇒ 15² = 12² + CD²

⇒ 225 = 144 + CD²

⇒ CD² = 81

⇒ CD = 9 cm

Total length of BC = BD + CD

= 5 + 9

= 14 cm