ΔABC is an isosceles triangle with AB = AC = 13 cm and the length of altitude from A on BC is 5 cm. Then, BC = ?
The given triangle is isosceles so the altitude from the one of the vertex is median for the side opposite to it.
AB = AC = 13 cm
h = 5 cm (altitude)
Δ ABX is a right angled triangle, right angled at X
(AB)2 = h2 + (BX)2 (BX = 1/2 BC)
169 = 25 + (BX) 2
BX = 12
⇒ BC = 24
10