A rectangle has twice the area of a square. The length of the rectangle is 12 cm greater and the width is 8 cm greater than a side of a square. Find the perimeter of the square.

Let length of a side of a square = x cm.

According to question,

Length of rectangle = (x + 12) cm

Breadth of rectangle = (x + 8) cm

Given,

⇒ Area of rectangle = 2 × area of square

⇒ (x + 12)(x + 8) = 2 × (x × x)

⇒ x(x + 8) + 12(x + 8) = 2x²

⇒ x² + 8x + 12x + 96 = 2x²

⇒ x² – 2x² + 8x + 12x + 96 = 0

⇒ -x² + 20x + 96 = 0

⇒ x² – 20x – 96 = 0

⇒ x² – 24x + 4x – 96 = 0

⇒ x(x - 24) + 4(x - 24) = 0

⇒ (x + 4)(x – 24) = 0

⇒ x + 4 = 0 or x - 24 = 0

⇒ x = -4 or x = 24 cm

Since, side of a square cannot be negative.

∴ x ≠ -4.

Side of square = 24 cm

Perimeter of square = 4 × side = 4 × 24

= 96 cm.

Hence, perimeter of square = 96 cm.