You can put this solution on YOUR website!
Let x = width of the pen.
If you have 500 feet of fence, then this is the perimeter, so
2W + 2L = 500
You need to find the length L in terms of x, remembering that x= width.
2x + 2L = 500 You have to solve for L.
Divide both sides by 2 to simplify things a bit:
x + L = 250
Subtract x from each side
So, now you have a formula for Area in terms of x:
To find the maximum area, you can graph this equation. I recommend that you graph this from x=0 to about x=250. It can't go past these values for x, right?
Now, (did you say that you know what the maximum is? It's a square, so each side will be 500/4 = 125, and the area will be 125^2 = 15625!!) graph y values from y=0 up to about 16000. The graph in this window should look like this:
This confirms that the maximum occurs at x = 125, and the value there for the area is y = about 15,000 or 16,000. The exact value can be found by substituting x = 125 into the formula A = x(250-x).