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umka2103 [35]
3 years ago
5

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 doe

s not need any fencing.
What dimensions would guarantee that the garden has the greatest possible area?

Mathematics
1 answer:
kari74 [83]3 years ago
6 0

9514 1404 393

Answer:

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

Step-by-step 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.

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