The altitude drawn to the base of an isosceles triangle is 8 cm and the perimeter is 32 cm Find the ...........

Quantitative Aptitude ( CCS) Mensuration 2D

The altitude drawn to the base of an isosceles triangle is 8 cm and the perimeter is 32 cm. Find the area of the triangle.

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Explanation:

Let ABC be the isosceles triangle and AD be the altitude
Let AB = AC = x. Then, BC = (32 - 2x).
Since, in an isosceles triangle, the altitude bisects the base,
so BD = DC = (16 - x).
In triangle ADC,(AC)²=(AD)²+(DC)²
⇒x²=(8)²+(16−x)²⇒x=10
BC = (32- 2x) = (32 - 20) cm = 12 cm.
Hence, required area = 1/2*BC*AD=1/2*12*8=48cm²