Question

A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders straight river. What are the dimensions of the field that has the largest area

Answer 1

Let each side perpendicular to the river be "x".

Then the side parallel to the river is "2400-2x".

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Area = width*length

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A(x) = x(2400-2x)

A(x) = 2400x - 2x^2

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You have a quadratic with a = -2 and b = 2400

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Maximum Area occurs where x = -b/2a = -2400/(2*-2) = 600 ft. (width)

length = 2400-2x = 2400-2*600 = 1200 (length)

Answer 2

Step-by-step explanation:

The largest area occurs when x = 600 ft. We need to find y: y = 2400 − 2x = 2400 − 2(600) = 1200 ft. Hence, the dimensions of the field is 600 ft × 1200 ft.