SOLUTION: A carpenter is building a rectangle room with a fixed perimeter of 356 ft. What dimensions would yield the maximum area? What is the maximum area?

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Question 329416: A carpenter is building a rectangle room with a fixed perimeter of 356 ft. What dimensions would yield the maximum area?
What is the maximum area?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
THe perimeter of a rectangle is,
P=2L%2B2W=356
L%2BW=178
The area of a rectangle is,
A=L%2AW
From the perimeter equation,
L=178-W
Substitute into the area equation,
A=%28178-W%29W
Now the area is a function of one variable.
To find the maximum, take the derivative wrt W and set it equal to zero.
A=178W-W%5E2
dA%2FdW=178-2W=0
2W=178
W=89
Then from above,
L=178-89=89
The maximum area for a given perimeter is obtained using a square.
Amax=89%5E2=7921sq.ft.