2. A series of rectangular fenced pens is to be built, each using 1000 m of fencing. (a) Find the dimensions that will maximize the total area in each situation. I. a rectangular pen with no restrictions Il. a rectangular pen, divided into two equal parts Ill. a rectangular pen placed against a barn, so it only requires three sides to be fenced. (b) Consider the three situations in part a). Do you see a pattern? Explain. (c) Explain how you could find the dimensions if the pens were similar to those in part a) ii) but divided into four equal parts