The area of a square and rectangle are equal. The length of the rectangle is greater than the length of any side of the square by 5 cm and the breadth is less 3 cm. Find the perimeter of the rectangle.

Question: The area of a square and rectangle are equal. The length of the rectangle is greater than the length of any side of the square by 5 cm and the breadth is less 3 cm. Find the perimeter of the rectangle.

Solution:
Let, the length of each side of the square be x cm.
Then, the length of rectangle = (x + 5) cm
and its breadth = (x - 3) cm

ATQ,
(x + 5)(x - 3) = x²
⇒ x² + 5x - 3x - 15 = x²
⇒ 2x = 15
∴ x = 15/2

Length = (15/2) + 5 = 25/2 cm
Breadth = (15/2) - 3 = 9/2 cm

∴ Perimeter = 2(length + breadth) = 2 {(25/2) + (9/2)}
= 2 (34/2) = 34 cm