A farmer is constructing a rectangular pen by placing a fence on the boundary for dealing with his cattle. He will use a portion of the north side of his 100 feet long barn for one side of the pen and will need to construct a dividing fence perpendicular to the barn to make two enclosures for various purposes. If he has 360 feet of fencing, what are the dimensions (length and width) of the pen which will maximize the total area of the pens? Justify your answer.

Please show how the answer was obtained.