A garden is in the shape of a square with perimeter of 32 feet. The garden is surrounded by two fences. One fence is around the perimeter of the garden, whereas the second fence is two feet from the first fence on the outside. If the material used to build the two fences is $1.22 per foot, what is the total cost of the fences?
Thank you.
To find the total cost of the fences, we need to calculate the length of each fence and then multiply it by the cost per foot.
Given that the garden is in the shape of a square, we can find the length of one side of the square by dividing the perimeter by 4 (since all sides of a square are equal).
Perimeter of the square = 32 feet
Length of one side = Perimeter / 4 = 32 / 4 = 8 feet
The first fence surrounds the perimeter of the garden, so its length is the same as the perimeter of the garden.
Length of the first fence = Perimeter = 32 feet
The second fence is two feet outside the first fence on all sides. Since the garden is a square, the length of the second fence is the same as the length of one side of the square plus twice the two-foot gap on each side.
Length of the second fence = Length of one side + (2 * gap) + (2 * gap)
= 8 feet + (2 * 2 feet) + (2 * 2 feet)
= 8 feet + 4 feet + 4 feet
= 16 feet
Now, we can calculate the total cost of the fences by multiplying the length of each fence by the cost per foot.
Cost of the first fence = Length of the first fence * Cost per foot = 32 feet * $1.22/foot
Cost of the second fence = Length of the second fence * Cost per foot = 16 feet * $1.22/foot
Total cost of the fences = Cost of the first fence + Cost of the second fence
To find the total cost of the fences, we need to calculate the lengths of both fences and then multiply each length by the cost per foot.
First, let's find the length of the inner fence, which is around the perimeter of the garden. We know that the garden is in the shape of a square, so all four sides are equal. Let's denote the length of one side of the square as "x".
Since the perimeter of the garden is given as 32 feet, we can write the equation:
4x = 32
Divide both sides of the equation by 4:
x = 32/4
x = 8
So, each side of the garden measures 8 feet.
Now, let's find the length of the outer fence, which is two feet longer on each side compared to the inner fence.
The length of each side of the outer fence is equal to the length of each side of the inner fence plus two feet. So, the length of each side of the outer fence is (8 + 2) = 10 feet.
Since the outer fence has four sides, its total length is 4 * 10 = 40 feet.
Now let's calculate the total cost of both fences.
The cost per foot of the fences is given as $1.22. To find the total cost, we multiply the length of each fence by the cost per foot and then add the two costs together.
The cost of the inner fence is 8 * 1.22 = $9.76.
The cost of the outer fence is 40 * 1.22 = $48.80.
Finally, we add the costs of the two fences together to find the total cost:
9.76 + 48.80 = $58.56.
Therefore, the total cost of the two fences is $58.56.
2 between the fence would have an addition of 2 ft to each side of the garden 8ft.
32 +(32+8) = 72 ft
72(1.22) =$ 87.84