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

Quantitative Aptitude ( CCS) Mensuration 2D

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

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Explanation:

let ABC be the isosceles triangle, the AD be the altitude
Let AB = AC = x then BC= 32-2x [because parameter = 2 (side) + Base]
since in an isoceles triange the altitude bisects the base so
BD = DC = 16-x
In a triangle ADC, (AC)^2=(AD)^2+(DC)^2
x^2=8^2+(16−x)^2
⇒x=10
BC = 32-2x = 32-20 = 12 cm
Hence, required area = (1/2)*BC*AD= (1/2)*12*10 = 60 sq cm