ΔABC is an isosceles triangle with AB = AC = 13 cm. The length of altitude from A on BC is 5 cm. Find BC.

Question

Philoid · Accepted Answer

Δ ABC is an isosceles triangle.

Also, AB = AC = 13 cm

Suppose the altitude from A on BC meets BC at D. Therefore, D is the midpoint of BC.

AD = 5 cm

ΔADB and ΔADC are right-angled triangles.

Applying Pythagoras theorem,

AB² = BD² + AD²

⇒BD² = 13² - 5²

⇒ BD² = 169 – 25 = 144

⇒ BD = 12 cm

So, BC = 2× 12 = 24 cm