Question

A contractor has 48 meters of fencing that he is going to use as the perimeter of a rectangular garden. The length of one side of the garden is represented by x, and the area of the garden is 108 square meters.
Determine, algebraically, the dimensions of the garden in meters.

Answer 1

Let the length of the garden be x and the width of the garden be y.

x*y = 108
2x + 2y = 48 giving x + y = 24 or y = 24 - x

substitute the second equation into the first,
x*(24-x) = 108
24x - x^2 = 108
x^2 - 24x + 108 = 0
(x-18)(x-6) = 0

So, x = 18 or x = 6.

But if x = 18, y = 6 and if x = 6, y = 18 so both solutions are actually the same with just the width and length swapped. So, your garden is 18 meters by 6 meters.