SOLUTION: Help please. A carpenter is building a rectangular room with a fixed perimeter of 160ft. What dimensions would yield the maximum area. What is the maximum area? The length that

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Question 460980: Help please.
A carpenter is building a rectangular room with a fixed perimeter of 160ft. What dimensions would yield the maximum area. What is the maximum area?
The length that would yield the maximum area is ___________feet, the width is___
The maximum area is ______sq feet
Thanks
Found 2 solutions by rwm, JimboP1977:
Answer by rwm(914) (Show Source):
You can put this solution on YOUR website!
max area of a rectangle is a square.
with a perimeter of 160 the square has sides of 40
the area is 40*40

Answer by JimboP1977(311) (Show Source):
You can put this solution on YOUR website!
2x+2y=160
160-2x = 2y
80-x = y
xy=A
x(80-x)=A
80x-x^2=A
Find gradient when zero ie the peak.
80-2x=0
x=80/2
x=40
So maximum area is 80*40-40^2 = 1600 square feet.
Width is 1600/40 = 40