The perimeter of a square is 48 cm. The area of a rectangle is 4 cm 2 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 = = 12 cm. By formula, Area = (side) 2 = 12 2 = 144 cm 2 . ∴ Area of rectangle = 144 – 4 = 140 cm 2 Let breadth of rectangle = x cm ∴ Length of rectangle = (x + 4) cm Area of rectangle = l × b = x(x + 4) cm 2 Substituting the values we get, ⇒ x(x + 4) = 140 ⇒ x 2 + 4x – 140 = 0 ⇒ x 2 + 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.

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Mathematics

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.

Mensuration

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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.