The length of a rectangular garden is 12m 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 the value of breadth be x metre

So, length = (x + 12) metre

Perimeter = 2(Length + Breadth) = 2(x + x + 12) = 2(2x + 12) = (4x + 24) metre

Area = Length $\times$ Breadth = x(x + 12) = (x² + 12x) metre²

Given, area is equal to 4 times the perimeter

∴ x² + 12x = 4(4x + 24)

$\Rightarrow x^2 + 12x = 16x + 96 \\[1em] \Rightarrow x^2 + 12x - 16x - 96 = 0 \\[1em] \Rightarrow x^2 - 4x - 96 = 0 \\[1em] \Rightarrow x^2 - 12x + 8x - 96 = 0 \\[1em] \Rightarrow x(x - 12) + 8(x - 12) = 0 \\[1em] \Rightarrow (x - 12)(x + 8) = 0 \\[1em] \Rightarrow x - 12 = 0 \text{ or } x + 8 = 0 \\[1em] x = 12 \text{ or } x = -8 \\[1em]$

Since, breadth cannot be negative hence, x ≠ -8

∴ x = 12 , x + 12 = 24

Hence, the length of the garden is 24m and breadth is 12m.