Question

Perimeter of isosceles triangle is 64 hight is 8 find area

Answer 1

AB = AC (Isosceles triangle)

BD = CD (Height AD bisects BC in Isosceles triangle)

Now, Let AB = AC = a, BC = b

=>2a + b = 64 (Perimeter)

=>b = 64 - 2a

=>b/2 = 32 - a -----Eq 1

=>8² + (b/2)² = a² (ADC is Right angled triangle)

=> 64 + (32 - a)² = a² (From Eq 1)

=> 64 + 1024 + a² - 64a = a²

=> 64a = 1088

=> a = 17