Final answer:
To find the width of the walkway around the pool, we need to calculate the combined area of the pool and walkway. Setting up an equation and solving for x, we find that the walkway should have a width of 2.5 feet.
Step-by-step explanation:
To find the width of the walkway, we can start by calculating the area of the pool. The pool is a rectangle with dimensions 9 feet by 8 feet, so the area is 9 feet * 8 feet = 72 square feet. Next, we need to find the area of the pool and the walkway combined. If the total area is 210 square feet and the pool area is 72 square feet, then the area of the walkway is 210 square feet - 72 square feet = 138 square feet. Since the walkway goes around the pool, its width adds to both the length and width of the pool. Let's assume the width of the walkway is x feet. This means the new length of the rectangle will be 9 feet + 2x feet (since there are two sides that are extended by x feet) and the new width of the rectangle will be 8 feet + 2x feet. Now we can set up an equation to solve for x:
(9 + 2x)(8 + 2x) = 138
Expanding the equation:
72 + 26x + 4x^2 = 138
Rearranging the equation:
4x^2 + 26x + 72 - 138 = 0
Simplifying the equation:
4x^2 + 26x - 66 = 0
Factoring the equation or using the quadratic formula, we find that x = 2.5 or x = -6.5. Since the width cannot be negative, the walkway should have a width of 2.5 feet.