a. A rectangular pen is built with one side against a barn. If 600 m of fencing are used for the other three sides of the pen, what dimensions maximize the area of the pen? b. A rancher plans to make four identical and adjacent rectangular pens against a barn, each with an area of 100 m² (see figure). What are the dimensions of each pen that minimize the amount of fence that must be used? Barn 100 100 100 100 a. To maximize the area of the pen, the sides perpendicular to the barn should be 150 m long and the side parallel to the barn should be 300 m long. (Type exact answers, using radicals as needed.) b. To minimize the amount of fence that must be used, each of the sides perpendicular to the barn should be m long and each of the sides parallel to the barn should be m long. (Type exact answers, using radicals as needed.)