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Question

# Solve the given problem.A farmer has a thousand feet of fence to enclose a rectangular area. What dimensions for the rectangle result in the maximum area enclosed by the fence?

Solution

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$2x+2y=1000$

$2y=1000-2x$

$y=\dfrac{1000-2x}{2}=\dfrac{2(500-x)}{2}=500-x$

Let's note:

$x$=one side of the rectangle.

$y$=the other side of the rectangle As the perimeter is 1000, we express the side $y$ in terms of $x$:

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