Problem 1. What is the maximum area that can be enclosed by a fence of fixed length if the fence is to be placed along a river so that only three sides of the rectangular area will be fenced? See the following diagram.

Problem 2. The frame for a kite is to be made from six pieces of wood. The four exterior pieces have been cut to the lengths indicated in the figure at the right. To maximize the area of the kite, how long should the diagonal pieces be? See the diagram at the right.

Problem 3. Find the dimensions of the largest isosceles triangle that can be inscribed in a circle of radius 4 centimeters.

Problem 4. Find the length of the shortest ladder that will reach over an 8-foot high fence to a large wall that is 3 feet behind the fence. See the diagram at the right.