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.
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