A contractor has 48 meters of fencing 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

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02-06-2016
Mathematics

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A contractor has 48 meters of fencing 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

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Hagrid Hagrid · Answer 1 · 2016-06-09T03:53:02+02:00

if we let y be the dimension of the other side, then the perimeter has the formula
P = 2x + 2y
48 = 2x + 2y

The area of the rectangle has the formula
A = xy
108 = xy

So,
x = 108/y

Substituting this to the first equation
48 = 2(108/y) + 2y
48y = 216 + 2y^2
2y^2 - 48y + 216 = 0

Solving the quadratic equation:
y = 18 or 6

Either of the two is the correct answer for y, the value of x would just be the other. So, the dimensions of the garden is
18 m x 6 m