Let's say the area of the rectangle is given by A = L*W, and the perimeter P is given by P = 2L + 2W, where L is rectangle's length and W is the width.
If the fence encloses the rectangle up against the wall it's perimeter will be P - L (since the wall side doesn't need fencing). But the fence length is 220 meters, which means:
P - L =220 --> 2L +2W - L =220 --> L +2W = 220 --> L = 220 - 2W.
If we plug the above equation into the formula of the area, we obtain: A = (220 - 2W)*W.
We may now consider A to be a function of width W only, written as A(W) = (220 - 2W)*W = 220W - 2W2.
Now to find the maximum value for the area A, we may set to zero the derivative of A(W) with respect to the variable W, that is: dA/dW = 220 - 4W = 0 --> W=55.
This means that: L = 220 - 2*55 = 110 and the maximum area A(W=55) = 110*55= 6050.
