Let ABC be the isosceles triangle whose sides are AB = AC = 25cm, BC = 14cm.

Let us draw altitude AD such that AD ⊥ BC.

We know that altitude bisects the opposite side.

So, BD = DC = 7cm.

In ADC, ∠ADC = 90°.

We know that the Pythagoras Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

So, by applying Pythagoras Theorem,

AC² = AD² + DC²

(25 cm)² = AD² + (7 cm)²

625 cm² = AD² + 49 cm²

AD² = 576 cm²

AD = 24 cm

The length of altitude is 24 cm.