Question

A rectangular garden measuring 12 meters by 16 meters is to have a walkway installed around it with a width of x meters, as shown in the diagram below. Together, the walkway and the garden have an area of 396 square meters. Write an equation that can be used to find x, the width of the walkway.

Answer 1

Equation that can be used to get x is; x2 + 14x - 51 = 0

Value of x (width of the walkway) = 3 meters

Explanation:

Since the width of the walkway is x m, then;

The length of the rectangle is (2x + 16) and

The width of the rectangle is (2x + 12). The area of the rectangle is 396.

Therefore;

(2x + 16)(2x + 12) = 396

4x2 + 24x + 32x + 192 = 396

4x2 + 56x - 204 = 0

x2 + 14x - 51 = 0

(x + 17)(x - 3) = 0

x + 17 = 0 or x - 3 = 0

x = -17 or x = 3

Discard the negative value and you are left with the width of the walkway being 3 meters wide.