Question

A gardener has 640 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing.

What dimensions would guarantee that the garden has the greatest possible area?

Answer 1

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Answer:

• 160 ft (out from the river)
• 320 ft (parallel to the river)

Explanation:

Let x represent the length of fence parallel to the river. Then the dimension of perpendicular to the river will be half the remaining fence: (640-x)/2. The total area will be ...

A = x(640-x)/2

This is the equation of a parabola that opens downward. It has zeros at x=0 and x=640, so its axis of symmetry is x = (0+640)/2 = 320. That is, the peak of the area curve is found when x=320.

The dimensions of the garden with the largest area are 160 ft wide by 320 ft long, where the long side is the river side.