2b) A farmer is building a pen inside a barn. The pen will be in the shape of a right triangle.

The farmer has 14 feet of barn wall to use for one side of the pen and wants another side of the pen to be 15 feet long.

a. To the nearest tenth of a foot, find all possible lengths for the third side of the triangle.

b. The farmer wants the area of the pen to be as large as possible. What length should he choose for the third side? Justify your answer.