Answer:
the width of the walkway should be approximately 8.60 feet.
Explanation:
To determine the width of the walkway, we need to subtract the area of the pool from the total area of the pool and the walkway.
The pool has dimensions of 9 feet by 10 feet, so its area is 9 feet * 10 feet = 90 square feet.
Let's assume the width of the walkway is "w" feet.
The area of the pool and the walkway is given as 650 square feet.
Therefore, the area of the walkway can be represented as (9 + 2w) feet * (10 + 2w) feet.
The equation can be set up as follows:
(9 + 2w) * (10 + 2w) - 90 = 650
Expanding the equation:
90 + 18w + 20w + 4w^2 - 90 = 650
Combining like terms:
4w^2 + 38w = 650
Rearranging the equation:
4w^2 + 38w - 650 = 0
Now we can solve this quadratic equation to find the width of the walkway.
Using the quadratic formula: w = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 4, b = 38, and c = -650.
Plugging these values into the quadratic formula:
w = (-38 ± √(38^2 - 4 * 4 * -650)) / (2 * 4)
Simplifying further:
w = (-38 ± √(1444 + 10400)) / 8
w = (-38 ± √11844) / 8
w = (-38 ± 108.83) / 8
Now we calculate both possible solutions:
w1 = (-38 + 108.83) / 8 ≈ 8.60 feet
w2 = (-38 - 108.83) / 8 ≈ -18.60 feet (discard this negative value)
Therefore, the width of the walkway should be approximately 8.60 feet.