Puzzle #5: The Back 40

Farmer Brown has decided to fence the inside of the back 40.  The back 40 is the square ABCD.  Farmer Brown plans to run one fence parallel to AB and another parallel to AD to divide the back 40 into four rectangles.  The fences will start at points on AD and AB the same distance from A.  Farmer Brown wants the area of  the rectangle bordering B to have the maximum area it can.  Where should the fences go?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, July 10, 2013 at noon Pacific Time. I will post the answer shortly after.