Manuel plans to install a fence around the perimeter of his yard. His yard is shaped like a square and has an area of 40,000 square feet. The company that he hires charges $2.50 per foot for the fencing and $50.00 for the installation fee.
Write a function, g(x), to represent the amount of money Manuel would be charged based on the number of feet of fence installed, x.
Determine the cost of the fence needed to install around the perimeter of Manuels yard.
x^2 = 40000
x =200
It is a square so you have 800 feet.
g(x) = 800(2.50) + 50
complete the math to see the cost.
To determine the cost of the fence needed to install around the perimeter of Manuel's yard, we first need to calculate the length of one side of the square yard.
Let's suppose the length of one side of the square yard is "L" feet.
Since the area of the square yard is given as 40,000 square feet, we can use the formula for the area of a square:
Area = Length * Width
40,000 = L * L
L^2 = 40,000
Taking the square root of both sides, we get:
L = √(40,000)
L ≈ 200 feet
Now that we know the length of one side, we can calculate the perimeter of the yard by multiplying the length of one side by 4 (since a square has equal-length sides):
Perimeter = 4 * L
Perimeter = 4 * 200
Perimeter = 800 feet
So, the perimeter of Manuel's yard is 800 feet.
Now, let's write the function g(x) to represent the amount of money Manuel would be charged based on the number of feet of fence installed, x.
The cost of the fencing is $2.50 per foot, and there is also a $50.00 installation fee. Therefore, the function g(x) can be defined as:
g(x) = 2.50x + 50.00
where x represents the number of feet of fence installed.
To determine the cost of the fence needed to install around the perimeter of Manuel's yard, we need to substitute x with the perimeter value we calculated earlier:
g(800) = 2.50 * 800 + 50.00
g(800) = $2,000 + $50
g(800) = $2,050
Therefore, the cost of the fence needed to install around the perimeter of Manuel's yard is $2,050.