If the diagonal of a rectangle is 10 cm long and its perimeter is 32 cm. Find the area of the rectangle.

Question: If the diagonal of a rectangle is 10 cm long and its perimeter is 32 cm. Find the area of the rectangle.

Solution:
let length = x and breadth = y
2(x + y) = 32
⇒ x + y = 16

x² + y² = 10²
= 100

now (x + y)² = 16²
⇒ x² + y² + 2xy = 256
⇒ 100 + 2xy = 256
⇒ 2xy = 256 - 100 = 156
⇒ xy = 78

∴ area = xy = 78 sq.cm