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

• A. 60
• B. 80
• C. 50
• D. 70

Answer: (A)

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,  A C 2 = A D 2 + D C 2   x 2 = 8 2 + 16 - x 2   ? x = 10   BC = 32-2x = 32-20 = 12 cm  Hence, required area =  1 2 * B C * A D =  1 2 * 12 * 10  = 60 sq cm