SOLUTION: A rectangular has a perimeter of 120 ft. Find the width if area is area is to be maximum.?

Algebra ->  Rectangles -> SOLUTION: A rectangular has a perimeter of 120 ft. Find the width if area is area is to be maximum.?      Log On


   

Question 875777: A rectangular has a perimeter of 120 ft. Find the width if area is area is to be maximum.?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
P=2L%2B2W=120
L%2BW=60
For a rectangle,
A=L%2AW
From above,
L=60-W
Substituting,
A=%2860-W%29W
A=60W-W%5E2
TO find the maximum, take the derivative and set it to zero.
dA%2FdW=60-2W
60-2W=0
2W=60
W=30
L=30
The maximum area occurs when the rectangle is a square.