The perimeter of a square is 48 cm. The area of a rectangle is 4 cm² less than the area of the square. If the length of the rectangle is 4 cm greater than its breadth, find the perimeter of the rectangle.

Perimeter of a square = 48 cm

Length of side of square = $\dfrac{\text{Perimeter}}{4} = \dfrac{48}{4}$ = 12 cm.

By formula,

Area = (side)² = 12² = 144 cm².

∴ Area of rectangle = 144 – 4 = 140 cm²

Let breadth of rectangle = x cm

∴ Length of rectangle = (x + 4) cm

Area of rectangle = l × b = x(x + 4) cm²

Substituting the values we get,

⇒ x(x + 4) = 140

⇒ x² + 4x – 140 = 0

⇒ x² + 14x – 10x – 140 = 0

⇒ x(x + 14) – 10(x + 14) = 0

⇒ (x + 14)(x – 10) = 0

⇒ x + 14 = 0 or x - 10 = 0

⇒ x = -14 or x = 10

Since, breadth cannot be negative.

∴ x ≠ -14.

Breadth = x = 10 cm and Length = x + 4 = 10 + 4 = 14 cm

Perimeter of rectangle = 2(l + b)

= 2(14 + 10)

= 2 × 24 = 48 cm.

Hence, perimeter of rectangle = 48 cm.