SOLUTION: what are the dimension of the largest rectangular field that can be enclosed with 60 meter of wire

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Question 1104503: what are the dimension of the largest rectangular field that can be enclosed with 60 meter of wire
Answer by math_helper(2461) About Me  (Show Source):
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Let the dimensions be L, W, and the area A.
+L+=+%2860-2W%29%2F2+=+30+-+W+
+A+=+LW+=+%2830-W%29W++=+30W-+W%5E2+
Take the derivative of A with respect to W:
+dA%2FdW+=+30-2W+
Set it to zero:
++++30-2W+=+0++ —> +W=15m+ —> +L=15m+
To show that's a max, note
+d%5E2A%2FdW%5E2+=+-2+ which indicates the curve is concave down (hence max at W=L=15)
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Ans: The dimensions of the largest rectangle is 15m x 15m
( Notice how it is a square that maximizes the area )
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