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?

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) (Show Source): You can put this solution on YOUR website!

For a rectangle, the perimeter is

Substitute this into the area equation,

To find the maximium area, take the derivative and set it to zero.

so you know that the value you get is a maximum (2nd derivative test).

The rectangle with the most area is actually a 125' x 125' square.
Answer by richwmiller(17219) (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

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