Pen problems a. A rectangular pen is built with one side against a barn. Two hundred meters 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? c. Two rectangular pens arc built against a bam. Two hundred meters of fencing are to be used for the three sides and the diagonal dividing fence (see figure). What dimensions maximize the area of the pen?

Solution Step 1: (a)A rectangular pen is built with one side against a barn. 200 meters of fencing are used for the other three sides of the pen. We have to find the dimensions that maximize the area of the pen Sketch the rough graph of rectangle pen from given data