Adam V. answered • 11/28/16

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The two equations needed to solve this problem are as follows:

Let L = the length of the rectangle

Let W = the width of the rectangle

Perimeter of a rectangle:

P = L+L+W+W = 2L+2W

Area of a rectangle:

A = L*W

We are told that the perimeter of the fencing = 96. Therefore:

2L + 2W = 96

L + W = 48

L = 48 - W

We are also told that the area of the fencing is 540 sq ft. Therefore,

L*W = 540

We now have two equations and two unknowns, so we can solve.

Substitute L into the second equation:

(48 - W)W = 540

-W

^{2}+ 48W = 540W

^{2}- 48W = -540W

^{2}- 48W + 540 = 0(W-30)(W-18) = 0

Therefore W either equals 30 or 18.

We know that L + W = 48.

If L = 30, then W = 18

If W = 30, then L = 18

Therefore, the dimensions of the fencing are 30 x 18