Question

In an isosceles triangle ABC, if AB = AC = 13 cm and the altitude from A on BC is 5 cm, find BC.

Answer 1

In ΔADB, by Pythagoras theorem

AD² + BD² = 13²

⇒ 25 + BD² = 169

⇒ BD² = 169 − 2 = 144

⇒ BD = `sqrt144` = 12 cm

In ΔADB and ΔADC

∠ADB = ∠ADC                       [Each 90°]

AB = AC                               [Each 13 cm]

AD = AD                               [Common]

Then, ΔADB ≅ ΔADC               [By RHS condition]

∴ BD = CD = 12 cm               [By c.p.c.t]

Hence, BC = 12 + 12 = 24 cm