SOLUTION: 100m of wire is available for fencing a rectangular piece of land. find the dimension of land which maximize the area. hence, determine the maximum area of the fence.
Question 1073354: 100m of wire is available for fencing a rectangular piece of land. find the dimension of land which maximize the area. hence, determine the maximum area of the fence. Answer by math_helper(2461) (Show Source):
You can put this solution on YOUR website! 100m of wire is available for fencing a rectangular piece of land. find the
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If the fence shape must be rectangular, then a square maximizes the enclosed area.
—— Proof that a square maximizes area ——
Perimeter = P = 2L + 2W
Area = A = L*W
A = ((P-2W)/2)*W = (PW)/2 - W^2
dA/dW = P/2 - 2W
Set dA/dW = 0: P/2 - 2W = 0 —> W = P/4 —> L=P/4 so a square shape.
—— End proof —————
A square with sides will maximize the area, and that area will be
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To enclose the maximum area with no shape restrictions, a CIRCLE will do:
Circumference=
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Making a circle with radius 15.915m would give you an enclosed area of
