A farmer needs to enclose a rectangular pen to allow his daughter’s pet lamb to run around in. He finds 175 feet of fencing to use. He decides to use his barn as one side of the rectangle, so he just needs to use the fence to form the other three sides. What is the maximum area he can enclose, and what are the dimensions of the rectangular pen he creates?

A farmer needs to enclose a rectangular pen to allow his daughter’s pet lamb to run around in. He finds 175 feet of fencing to use. He decides to use his barn as one side of the rectangle, so he just needs to use the fence to form the other three sides. What is the maximum area he can enclose, and what are the dimensions of the rectangular pen he creates? Show all your work.