The length of a rectangular garden is 12 m more than its breadth. The numerical value of its area is equal to 4 times the numerical value of its perimeter. Find the dimensions of the garden.

Let breadth of rectangular garden = x meters,

∴ Length = (x + 12) meters.

Area of garden = length × breadth = x(x + 12) m²

Perimeter of garden = 2(l + b)

= 2[(x + 12) + x]

= 2[2x + 12] = (4x + 24) meters.

According to question,

⇒ Area of garden = 4 × Perimeter of garden

⇒ x(x + 12) = 4 × (4x + 24)

⇒ x² + 12x = 16x + 96

⇒ x² + 12x - 16x - 96 = 0

⇒ x² - 4x - 96 = 0

⇒ x² - 12x + 8x - 96 = 0

⇒ x(x - 12) + 8(x - 12) = 0

⇒ (x + 8)(x - 12) = 0

⇒ x + 8 = 0 or x - 12 = 0

⇒ x = -8 or x = 12.

Since, breadth cannot be negative.

∴ x ≠ -8.

Breadth = x = 12 m and Length = (x + 12) = (12 + 12) = 24 m.

Hence, length and breadth of garden are 24 m and 12 m respectively.