Designing Swimming Pools

A swimming pool is designed to have a rectangular top, a level shallow end bottom, and a flat, gradually sloping deep end bottom (see figure above). The width (5.5 feet) and height (3.25 feet) of the shallow end must always remain the same. The length of the shallow end and deep end can be modified according to the designer’s interests, as long as the volume of the pool equals 300 cubic feet, as required.

Can the pool contain only a shallow end? only a deep end? Explain why or why not.

What is the greatest possible depth of the pool? Explain your solution.

What is the greatest depth of the pool if half of the pool is shallow? Explain your solution.

This Geometer’s Sketchpad template may be helpful: