Chris wants to build a vegetable garden such that three sides of the garden are fenced in the fourth side of the garden will be exiting the back fence. He has 30 feet of fencing available find the dimensions of the garden that will produce the maximum enclosed area.
as always in such problems, the maximum area is achieved when the fence is divided equally among lengths and widths. In this case, that is 15 ft each.
The garden will be 15 x 7.5 ft
see similar questions below to see why this is so.
By the way, you kind of garbled the question, what with run-on sentences and "exiting the" back fence.