You have two variables here so we're going to use two equations, substitute, and then find the maximum. Start with area. If the width of the fence is x and the length is y, than . This is what you trying to maximize. Now let's talk about the perimeter. We have 600 ft. of fencing to use, thus we know that . From here, solve for a variable from the perimeter equation and substitute that into the area one so that the area equation has just one variable. Then take the derivative and you know the rest.

EDIT: Ooops. This is in the pre-calc forum. Do you know calculus?