A dog pen in the shape of a rectangle is to be built using one wall of a house as a side. If 132 feet of fencing is to be used and the pen is to provide the maximum room for the dog, how long should each side be? Solve in as many ways as you can.

Now try to find as many different lengths of fence as you can (other than 132 feet) that will give whole number pen sides. For each different fence length, give the lengths of each side that give the maximum room for the dog.