Question

In an isosceles triangle ABC, AB = AC = 25 cm, BC = 14 cm. Calculate the altitude from A on BC.

Answer 1

We have

AB = AC = 25 cm and BC = 14 cm

In ΔABD and ΔACD

∠ADB = ∠ADC [Each 90°]

AB = AC [Each 25 cm]

AD = AD [Common]

Then, ΔABD ≅ ΔACD [By RHS condition]

∴ BD = CD = 7 cm [By c.p.c.t]

In ΔADB, by Pythagoras theorem

AD² + BD² = AB²

⇒ AD² + 7² = 25²

⇒ AD² = 625 − 49 = 576

⇒ AD = `sqrt576` = 24 cm