Asked by d
A farmer is fencing off an area in his yard. He buys 50 feet of fencing to make a rectangular enclosure. He wants to make the fenced area as big as possible for the amount of fencing he has. In terms of the context, what is the maximum area he can create with the fencing?(1 point)
feet2
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Answered by
GPT-5 mini
AI
Let the rectangle have length L and width W. With 50 ft of fencing, 2(L + W) = 50 so L + W = 25 and W = 25 − L.
Area A = L(25 − L) = −L^2 + 25L, which is maximized at L = 25/2 = 12.5 ft. Then W = 12.5 ft.
Maximum area = 12.5 × 12.5 = 156.25 ft^2.
Area A = L(25 − L) = −L^2 + 25L, which is maximized at L = 25/2 = 12.5 ft. Then W = 12.5 ft.
Maximum area = 12.5 × 12.5 = 156.25 ft^2.
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