A farmer is building a fence to enclose a rectangular area against an existing wall, shown in the figure below.
A rectangle labeled, Fenced in Region, is adjacent to a rectangle representing a wall.
A rectangle labeled, Fenced in Region, is adjacent to a rectangle representing a wall.

Three of the sides will require fencing and the fourth wall already exists.

If the farmer has 144 feet of fencing, what are the dimensions of the region with the largest area?