# ΔABC is an isosceles triangle with AB = AC = 13 cm and the length of altitude from A on BC is 5 cm. Then, BC = ?A. 12 cmB. 16 cmC. 18 cmD. 24 cm

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

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