Mason has 108 feet of material to build a fence around a rectangular pool on his property. If the width of the fence must be 6 feet, what is the length of the fence in yards if he uses all 108 feet of material?
48 yards
16 yards
96 yards
32 yards
First, we need to find the perimeter of the rectangular pool. Let's call the length of the fence x. Then, we know that the width of the fence is 6 feet, so the width of the pool must be x - 12 (since the fence will be built 6 feet on either side of the pool).
The perimeter of the pool will be the sum of the lengths of all four sides:
P = x + (x - 12) + 6 + 6
Simplifying, we get:
P = 2x - 4
We know that Mason has 108 feet of material to work with, so we can set up the following equation:
108 = 2x - 4
Solving for x:
2x = 112
x = 56
So the length of the fence (which is equal to the length of the pool plus twice the width of the fence, or x + 12) is:
56 + 12 = 68 feet
To convert to yards, we divide by 3:
68 ÷ 3 = 22.67
Rounding to the nearest whole number, we get:
23 yards
So the answer is not one of the choices provided.
To find the length of the fence, we need to subtract twice the width of the fence from the total length of material.
Given that the width of the fence is 6 feet, the total length of material is 108 feet.
Let's calculate the length of the fence:
Length of the fence = Total length of material - 2 * Width of the fence
Length of the fence = 108 feet - 2 * 6 feet
= 108 feet - 12 feet
= 96 feet
To convert feet to yards, we divide by 3:
Length of the fence in yards = 96 feet ÷ 3
= 32 yards
Therefore, the length of the fence, if Mason uses all 108 feet of material, is 32 yards. Therefore, the correct answer is 32 yards.