SOLUTION: A farmer has 3000 feet of fencing available to enclose a rectangular field. What is the maximum area?
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Question 281331: A farmer has 3000 feet of fencing available to enclose a rectangular field. What is the maximum area?
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
It's a square.
750 on a side --> 562500 sq feet
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Do you need proof it's a square, or will you trust me?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A farmer has 3000 feet of fencing available to enclose a rectangular field. What is the maximum area?
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Perimeter = 2(L+W)
3000 = 2(L+W)
1500 = L+W
L = W-1500
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Area = W*L
A = W(W-1500)
A = W^2-1500W
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Quadratic equation with a = 1, b = -1500
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Maximum occurs when W = -b/2a = 1500/2 = 750 ft.
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Since L+W = 1500
L = 1500-750
L = 750ft
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Final Answer: length and width need both be 750'
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Cheers,
Stan H.
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