Question

Three neighbors plan to complete fencing projects this spring. As shown in the diagrams below, Neighbor A plans to fence in his rectangular backyard with a 6-foot tall wooden privacy fence. Neighbor B plans to construct a circular chain link fence around his pool. And, Neighbor C is putting a vinyl fence around three side of his front yard. Note: Diagrams are not drawn to scale. Intended fences are marked with a dashed line.

Which neighbor has the most amount of fence to put up?
Which neighbor has the least amount of fence to put up?

Answer 1

- The neighbor that has the most amount of fence to put up is: Neighbor A.

- The neighbor that has the least amount of fence to put up is: Neighbor C.

Explanation:

To calculate the amount of fence that Neighbor A has to put up, you need to add the following distances:

`Fence_A=5yards+8yards+25yards+8yards\\Fence_A=46yards`

Convert yards to feet (Remember that
`1yard=3feet`:

`Fence_A=(46yards)((3feet)/(1yard))=138feet`

To calculate the amount of fence that Neighbor B has to put up, you need to use the formula for calculate the circumference of a circle:

`C=2\pi r`

Where r is the radius.

In this case, the radius is:

`r=(30feet+10feet)/(2)=20feet`

Substituting, you get:

`C=Fence_B=2\pi (20feet)=125.66feet`

To calculate the amount of fence that Neighbor C has to put up, you need to add the following distances:

`Fence_C=16feet+58feet+16feet\\Fence_C=90feet`

Therefore, the neighbor that has the most amount of fence to put up is: Neighbor A.

The neighbor that has the least amount of fence to put up is: Neighbor C.