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

Given: 

Isosceles triangle ABC, where AB = AC = 13 cm and the altitude from A on BC is 5 cm. 

To find: 

The value of BC. 

Solution:

In ΔADB 

AD² + BD² = AB² 

5² + BD² = 13² 

25 + BD² = 169 

BD² = 169 - 25

BD² = 144 

BD = \(\sqrt{144}\)

BD=12cm 

In ΔADB and ΔADC 

∠ADB = ∠ADC = 90 

AB = AC = 13cm 

AD = AD (Common) 

ΔADB ≅ ADC (By RHS condition) 

BD = CD = 12cm (c.p.c.t) 

As BC = BD + DC 

BC = 12 + 12 

BC = 24cm