Questiona. A rectangular pen is built with one side against a barn. If 400 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 $225 \mathrm{~m}^{2}$. What are the dimensions of each pen that minimize the amount of fence that must be used? \begin{tabular}{|l|l|l|l|l|} \hline \multicolumn{4}{|c|}{ Bam } \\ \hline 225 & 225 & 225 & 225 \\ \hline \end{tabular} a. To maximize the area of the pen, the sides perpendicular to the barn should be 100 m long and the side parallel to the barn should be 200 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 33 m long and each of the sides parallel to the barn should be $3 \sqrt{5} \mathrm{~m}$ long. (Type exact answers, using radicals as needed.)