Question

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

Answer 1

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 

x2=8^2+(16−x)^2x2=8^2+16-x2 ⇒x=10⇒x=10 

BC = 32-2x = 32-20 = 12 cm 

Hence, required area = 1/2*BC*AD= 1/2*12*10 = 60 sq cm