Stanley wants to build a swimming pool. The municipal gov mandates that a fence must surround all outdoor swimming pools and that the enclosure created by this fence cannot exceed a perimeter of 150 meters. Stanley wants to create the biggest rectangular swimming space possible so they plan on using the full 150 meters of fencing, however, he also want a cement sidewalk of 1 meter width all around the swimming area of the pool (which is inside the fence too). Stanley’s family is in argument over who has the best pool. What is the dimensions of the POOL (but don’t forget the sidewalk surrounding it in your calculations) to maximize the swimming area. In your answer include:
A. Diagram of the pool (including the sidewalk around the swimming area) labeled in terms of x (use x as the shorter side along the outer edge of the sidewalk).
B. Your equation used for calculations A(x) = blank. Have the equation give the area for the entire pool region - swimming area + sidewalk surrounding.
C. A sketch of your graph, with the values for the y-intercept, roots and vertex labeled as well ad the axes.
D. What are the best dimensions of the entire swimming pool complex (pool and sidewalk).
