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?

Question

48 yards
16 yards
96 yards
32 yards

Answer 1

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.