You have a given length of fence.
Using the wall of a house as one side of a rectangular fence, how would you place
the fence around the other three sides in order to enclose the largest possible area?
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The amount of fencing is a constant, feet.
. . So we have: . .
The area of the region is: . .
Substitute  into : .
This is a parabola that opens downward.
. . Its maximum is at its vertex.
The vertex is at: .
. . So we have: .
We will use feet (a quarter of the fencing) for each of the two shorter sides
. . and the rest, feet, for the long side.