Final answer:
The length of the rectangular pool can be found by setting up and solving an equation. The width is assumed to be 'x' feet and the length is 8 feet more than the width. By setting up the equation x(x + 8) = 65 and solving for 'x', we find that the width of the pool is 5 feet and the length is b. 13 feet.
Step-by-step explanation:
To find the length of the rectangular pool, we need to set up an equation based on the given information. Let's assume the width of the pool is 'x' feet. According to the problem, the length is 8 feet more than the width, so the length would be 'x + 8' feet. The area of a rectangle is given by the formula length x width, so we can set up the equation:
x(x + 8) = 65
Simplifying the equation:
x^2 + 8x = 65
Now, let's solve the quadratic equation by setting it equal to zero:
x^2 + 8x - 65 = 0
Using factoring or the quadratic formula, we find that the solutions to this equation are x = 5 and x = -13. Since the width cannot be negative, the width of the pool is 5 feet. Therefore, the length of the pool would be 5 + 8 = 13 feet.