In this exercise, you will apply your new knowledge of polynomial operations to create a presentation on constructing a walkway for your friend. The presentation should include your answers to the steps below, as well as all mathematical work to support your answers and explanations. You may use PowerPoint (or similar software) to create your presentation.
A good friend of yours is planning to install a new concrete walkway around his backyard swimming pool. The pool measures 25 feet long by 15 feet wide, and the width of the walkway is to be the same all the way around. Your friend is trying to determine how wide to make his walkway and needs your advice.
1. Construct a diagram of the pool and walkway, labeling all known and unknown dimensions.
2. Write a polynomial expression to model the square feet of concrete needed.
3. Determine how much concrete is needed if the walkway is:
a.) 4 feet wide
b.) 5 feet wide
c.) 6 feet wide
Be sure to show your work.
4. Determine the price for #3 – parts a, b, and c given that the price per square foot of concrete is $25. Be sure to show your work.
5. Which sidewalk width would you recommend for your friend and why?