Question

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. Fin the dimensions
of the garden

Answer 1

Answer:

Let the breadth be x m. Then, length=(x+12) m.

Area = 4*Perimeter

x(x+12) = 4*2*(x + x+12)

x^2 + 12x = 8(2x+12)

x^2 + 12x = 16x + 96

x^2 - 4x - 96 = 0

x^2 - 12x + 8x - 96 = 0

x(x - 12) + 8(x - 12) = 0

(x - 12)(x + 8) = 0

x = 12 or x = 8.

Since x is the side of a rectangle, its value can not be lesser than 0.

Hence, x = 12.

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