SOLUTION: You have 50 yards (50-2x) of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area? This involves

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: You have 50 yards (50-2x) of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area? This involves       Log On


   

Question 881026: You have 50 yards (50-2x) of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area? This involves quadratic functions if that makes it easier to understand.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The perimeter of the rectangle is,
P=2%28L%2BW%29=50
L%2BW=25
The area of the rectangle is,
A=L%2AW
Substitute from above,
L=25-W
A=%2825-W%29W
A=25W-W%5E2
Differentiate with respect to W and set the derivative equal to zero.
dA%2FdW=25-2W=0
2W=25
W=25%2F2
Then,
L=25%2F2
The maximum area for a given perimeter is a square.