Question

(7 pts) A school has 400 feet of fencing to build a set of 3 athletic fields as shown below. What dimensions

should they use to build the largest possible athletic complex? Include appropriate units with your answer.
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Answer 1

Explanation:

the side lengths are (400 - 4x)/2 = 200 - 2x

A = x(200 - 2x)

A = 200x - 2x²

Maximum area will occur when the derivative is set to zero.

dA/dx = 200 - 4x

0 = 200 - 4x

x = 200/4 = 50 ft

each field will be 50 x 33⅓ ft.

total area will be 5000 ft²

Which is not very big for a sports complex. I've owned houses with more floor space than that.