Question

Suppose you bought a 100-foot fence that you wanted to put around a square section of yard that will be used as a garden. The side length of your garden is 13 feet. The fencing was on sale for $12.60 per foot.

How much fencing is left over? How much did you pay for the fencing you did not use? Show your work.

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Answer 1

To determine how much fencing is left over and how much you paid for the fencing you did not use, let’s first calculate the amount of fencing used for the square garden.

1. **Calculate the perimeter of the square garden:**

The formula for the perimeter (P) of a square is:

\[
P = 4 \times \text{side length}
\]

Given the side length of the garden is 13 feet:

\[
P = 4 \times 13 = 52 \text{ feet}
\]

2. **Calculate how much fencing is left over:**

You originally bought a 100-foot fence. After using 52 feet for the garden, the remaining fencing can be calculated as:

\[
\text{Remaining fencing} = \text{Total fencing} - \text{Fencing used}
\]

\[
\text{Remaining fencing} = 100 - 52 = 48 \text{ feet}
\]

3. **Calculate the cost of the fencing that was not used:**

The cost per foot of the fencing is $12.60. The cost of the remaining fencing can be calculated as:

\[
\text{Cost of unused fencing} = \text{Remaining fencing} \times \text{Cost per foot}
\]

\[
\text{Cost of unused fencing} = 48 \times 12.60
\]

Calculating that gives:

\[
48 \times 12.60 = 604.80
\]

4. **Summary of the results:**

- **Fencing left over:** 48 feet
- **Cost of fencing not used:** $604.80

Thus, you have 48 feet of fencing left over and the cost of the fencing you did not use is $604.80.