In a triangle ABC, AB = AC and the perimeter of ΔABC is 8(2 + √2) cm. If the length of BC is √2 times the length of AB, then find the area of ΔABC.

Solution (By Examveda Team)

Let the side of triangle be x, x & √2x
Perimeter = 8(2 + √2)
x + x + x√2 = 8(2 + √2)
2x + x√2 = 8(2 + √2)
x(2 + √2) = 8(2 + √2)
(comparing on both side)
x = 8
Area of ΔABC = $$\frac{1}{2}$$ × 8 × 8 = 4 × 8
= 32