A rectangular field is to be fenced off on three sides with the fourth side being the bank of a river. If the cost of the fence is $8 per foot for the two ends and $12 per foot for the side parallel to the river, what are the dimensions of the largest rectangle that can be enclosed with $3840 worth of fence

Question

Aydin

Mathematics

3 June, 16:04

A rectangular field is to be fenced off on three sides with the fourth side being the bank of a river. If the cost of the fence is $8 per foot for the two ends and $12 per foot for the side parallel to the river, what are the dimensions of the largest rectangle that can be enclosed with $3840 worth of fence

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Answers (1)

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Bailey Levine · Answer 1

120 x 160

Step-by-step explanation:

If the length of the two ends is x foot per end, and the length of the parallel side is y foot, you can write the following equations:

16x + 12y = 3840

area = x * y

Simplify and rewrite the first and combine with second:

y = 320 - 4/3x

area = 320x - 4/3x²

Now you have a quadratic equation of which you want the maximum.

[calculation omitted]

The top is reached for x = 120 and y=160

The area will then be 19,200 ft²