ExplanationThe two values given are the area of the park and three out of the four sides of the perimeter of the park. If the side without fencing is a length, the equation for the overall length of the existing fence is 180 = 2W + L, so L = 180 – 2W.

The equation for the area of the park is LW = 3,600. With two variables and two equations, it is now possible to solve for the possible values of L:

\(L \times W = 3,600 L = 180 - 2W\)

\((180 - 2W)W = 3,600\)

\(180W - 2W^2 = 3,600\)

\(90W - W^2 = 1,800\)

\(0 = W^2 - 90W + 1,800\)

\(0 = (W - 60)(W - 30)\)

So W = 30 or 60. Plug each value back into either of the original two equations to solve for the corresponding length, which is 120 or 60, respectively.

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Sandy

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