SOLUTION: find the dimension and maximum area of a rectangle if its perimeter is 36m.

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Question 900801: find the dimension and maximum area of a rectangle if its perimeter is 36m.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let L and W be the length and width of the rectangle.
The perimeter is,
P=2L%2B2W=36
So,
L%2BW=36
The area of the rectangle is,
A=L%2AW
From the perimeter,
L=36-W
Substitute,
A=%2836-W%29W=36W-W%5E2
To find the extremum, set the derivative of A equal to zero.
dA%2FdW=36-2W
36-2W=0
2W=36
W=18
So then,
L%2B18=36
L=18
The maximum area for a given perimeter is actually a square.
A%5Bmax%5D=18%5E2=324m%5E2