All 50 states have legislation regarding pool safety, the majority of which includes a requirement for a safety fence around the perimeter of the top of an in-ground pool.

If a rectangular in-ground pool has a length that is 2 feet less than twice its width, and the area of the top of the pool is 480 square feet, how many linear feet of fencing are required, assuming the fence is placed 1 foot from the edge of the water on all sides?

A) 92
B) 100
C) 108
D) 116

To solve this problem, we can set up an equation to find the dimensions of the rectangular in-ground pool. Then, we can calculate the perimeter of the top of the pool and add the required safety fence to find the total linear feet of fencing needed.

Explanation:

To find the dimensions of the rectangular in-ground pool, we can set up an equation using the information given. Let's let the width of the pool be 'w'. The length of the pool will then be 2w - 2 feet. The area of the pool is given as 480 square feet, so we can write the equation: w * (2w - 2) = 480. Solving this quadratic equation, we find w = 16 and 6 (the negative solution is discarded as it doesn't make sense in this context).

Now that we know the width is 16 feet, we can calculate the length to be 2 * 16 - 2 = 30 feet. The perimeter of the top of the pool is then 2 * (16 + 30) = 92 feet.

To determine the length of the required safety fence, we need to add 2 feet to each side of the pool's perimeter, as the fence is placed 1 foot from the edge of the water on all sides. Therefore, the total linear feet of fencing required is 92 + 2 + 2 + 2 + 2 = 100 feet.

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