SOLUTION: You have 500 ft of fencing all rolled up and you want to make a rectangular playground area for your son. What are the dimensions of the largest playground you could build?

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Question 258860: You have 500 ft of fencing all rolled up and you want to make a rectangular playground area for your son. What are the dimensions of the largest playground you could build?
Found 2 solutions by Fombitz, richwmiller:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A=L%2AW
For a rectangle, the perimeter is
P=2%2A%28L%2BW%29=500
L%2BW=250
L=250-W
Substitute this into the area equation,
A=%28250-W%29W=250W-W%5E2
To find the maximium area, take the derivative and set it to zero.
dA%2FdW=250-2W=0
d2A%2Fdw2=-2 so you know that the value you get is a maximum (2nd derivative test).
250-2W=0
+2W=250
W=125
L=250-W=125
The rectangle with the most area is actually a 125' x 125' square.

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
What do you mean by largest? Largest in length? largest in area?
The rectangle with the largest area will be a square.
4a=500
a = 125, area = 15625