Question

The altitude drawn to the base of a isosceles triangle is 8 cm and 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)2AC2=AD2+DC2 

x2=82+(16−x)2x2=82+16-x2 ⇒x=10⇒x=10 

BC = 32-2x = 32-20 = 12 cm 

Hence, required area = 12*BC*AD12*BC*AD= 12*12*1012*12*10 = 60 sq cm