George has enough fencing to enclose 2400 square feet around a circular pool. If he builds a circular fence and he wants 12 foot walkway around the pool, what is the largest pool diameter possible?

Area = πr^2

2400 = 3.14r^2

r^2 = 764

r = 27 2/3

Solve for r. d = 2r therefore d =

Assuming the walkway is completely around the pool and within the fence, largest pool diameter is d-24.

Area = πr^2

2400 = 3.14r^2

r^2 = 764

r = 27 2/3

Solve for r. d = 2r therefore d = 55 1/3

Assuming the walkway is completely around the pool and within the fence, largest pool diameter is d-24.

To find the largest pool diameter possible, we need to understand the relationship between the pool's area, the walkway's width, and the fencing required.

First, let's find the area of the circular pool. The formula for the area of a circle is π * r^2, where π is a mathematical constant approximately equal to 3.14159 and r is the radius of the pool.

Since George wants a 12-foot walkway around the pool, we need to increase the pool's radius by 12 feet to accommodate the walkway. So, the radius of the pool will be r + 12.

The area of the pool, including the walkway, can be calculated as (π * (r + 12)^2).

Now, let's take a look at the fencing required. The circumference of a circle can be calculated using the formula 2 * π * r. Since George wants to enclose 2400 square feet, the circumference of the fence will be equal to the perimeter of the pool plus the walkway. Therefore, the fence's circumference will be 2 * π * (r + 12).

Now, we'll equate the fence's circumference to the fencing George has, which is enough to enclose 2400 square feet. So,
2 * π * (r + 12) = 2400.

Simplifying the equation, we have:
2 * (3.14159) * (r + 12) = 2400.

Now we can solve for r, the radius of the pool:
6.28318 * (r + 12) = 2400,
(r + 12) = 381.92,
r = 369.92.

Since the diameter is twice the radius, the largest pool diameter possible would be 2 * 369.92 = 739.84 feet (approximately).