Answer :
"
Final answer:
The number of linear feet of fencing required, assuming the fence is placed 3 feet from the edge of the water on all sides, is 80 feet.
Explanation:
To find the dimensions of the rectangular in-ground pool, we can set up an equation using the given information. Let's assume the width of the pool is x feet.
According to the given information, the length of the pool is 2 feet less than twice its width. So, the length can be expressed as 2x - 2 feet.
We are also given that the area of the top of the pool is 480 square feet. The formula for the area of a rectangle is length multiplied by width. So, we can set up the equation:
x(2x - 2) = 480
Simplifying the equation, we get:
2x^2 - 2x = 480
Now, let's solve this quadratic equation to find the value of x.
After solving the equation, we find that x = 12.
Therefore, the width of the pool is 12 feet and the length is 2(12) - 2 = 22 feet.
To calculate the perimeter of the pool, we add up all the sides. The perimeter is given by the formula:
Perimeter = 2(length + width)
Substituting the values, we get:
Perimeter = 2(22 + 12) = 2(34) = 68
Since the fence is placed 3 feet from the edge of the water on all sides, we need to add an additional 3 feet to the perimeter.
Therefore, the total linear feet of fencing required is 68 + 3 + 3 + 3 + 3 = 80.
Learn more about calculating the amount of fencing required for a rectangular in-ground pool here:
https://brainly.com/question/28213091
#SPJ14
"
Final answer:
The number of linear feet of fencing required, assuming the fence is placed 3 feet from the edge of the water on all sides, is 104 feet.
Explanation:
To find the dimensions of the rectangular in-ground pool, we can set up an equation using the given information. Let's assume the width of the pool is x feet. According to the given information, the length of the pool is 2 feet less than twice its width, which can be expressed as 2x - 2 feet.
The area of the pool is given as 480 square feet. We can use the formula for the area of a rectangle, which is length multiplied by width, to set up an equation:
x(2x - 2) = 480
Simplifying the equation, we get:
2x^2 - 2x - 480 = 0
We can solve this quadratic equation by factoring or using the quadratic formula. The solutions are x = 16 and x = -15. Since the width cannot be negative, we discard the negative solution.
Therefore, the width of the pool is 16 feet. Using the given relationship, we can calculate the length as 2(16) - 2 = 30 feet.
Now, to find the perimeter of the pool, we add up the lengths of all the sides:
Perimeter = 2(length + width) = 2(30 + 16) = 92 feet.
Since the fence is placed 3 feet from the edge of the water on all sides, we need to add 3 feet to each side of the pool. Therefore, the total length of fencing required is 92 + 3 + 3 + 3 + 3 = 104 feet.
Learn more about calculating the amount of fencing required for a rectangular in-ground pool here:
https://brainly.com/question/28213091
#SPJ14