Ina n isosceles triangle ABC, AB = AC and AD is perpendicular to BC at D. If AD = 8 cm and perimeter of ΔABC is 64 cm, then the area of ΔABC is:

120 cm²

Let, AB = AC = x

BD = y

We know that,

Perimeter is the total sum of all the sides.

BD = DC

According to the question,

x + x + y + y = 64

x + y = 32

x = 32 - y

From ΔABD,

x² = y² + 8²

(32 - y)² = y² + 8²

32² - 64y + y² = y² + 64

64y = 1024 - 64

y = 15 = BD

Now,

BC = 2 × BD  = 2 × 15 = 30 cm 

Area of triangle ABC  = \(\frac{1}{2}\) × 30 × 8 = 120 cm²