determining the dimensions of a pool

Question

There will be a rectangular pool with two square gardens at each end of the pool.The pool and garden can be as wide as the owner wants but must not exceed 140 ft. How do I determine the width and length of the pool that'll determine the maximum area?

Answer 1

Answer 2

Divide the maximum allowed length of 140 ft into 3 equal widths. This will make the width of the pool 46 2/3 feet, and the width of each garden 46 2/3 feet. Since the gardens are squares, their lengths are also 46 2/3 feet. This actually makes 3 squares all next to each other: the first garden, the pool, and the second garden are all squares. Remember that squares are technically rectangles so this is allowed for the pool's shape, and we wanted the thinnest pool allowed. This gives the maximum total area possible, which will be 140 x 46 2/3 which equals 6,533 1/3 square feet.

Draw it and see! Then make another drawing with different measurements to check and make sure our answer still produces the largest total area. For instance if each garden was 20x20 feet and the pool was 100ft long, that total length equals 140, but the total area would only be 2,800 square feet. Or if the pool was 138 ft long and each garden was 1 ft long the total area would only be 140 square feet. Or if the pool was 50 feet long and each garden was 45 feet long the total area would only be 6,300 square feet.