SOLUTION: Find the rectangle of perimeter l which has the maximum area

Question 1087451: Find the rectangle of perimeter l which has the maximum area
Found 2 solutions by Alan3354, math_helper:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find the rectangle of perimeter l which has the maximum area
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The max area of a rectangle of given perimeter is a square.
You can believe that, or I can prove it.
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P = 1 = 4s --- s = side length
s = 1/4

Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
Max area is when the rectangle is a square: L=W=
�
Proof: 2L + 2W = 1 �>
A = LW =
Take derivative of A with respect to L:
dA/dL =
Set that to 0 and solve for L, while noting that �> Concave down so our answer will give us a MAX:

�>

Since L=W we have a square.

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