Question

14
Essay 5 points
1. 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 was paid for the unused fencing, let's go through the calculations step by step.

### Step 1: Calculate the perimeter of the garden
The garden is square-shaped, and the side length is given as 13 feet. The formula for the perimeter \( P \) of a square with side length \( s \) is:

\[
P = 4s
\]

Substituting the side length into the formula:

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

### Step 2: Calculate the amount of fencing left over
You initially bought 100 feet of fencing. Now, we find out how much fencing is left after using some for the garden:

\[
\text{Fencing left over} = \text{Initial fencing} - \text{Perimeter used}
\]

Substituting the values:

\[
\text{Fencing left over} = 100 - 52 = 48 \text{ feet}
\]

### Step 3: Calculate the cost of the fencing not used
The cost of the fencing is given as $12.60 per foot. To find the total cost of the leftover fencing, we calculate:

\[
\text{Cost of unused fencing} = \text{Fencing left over} \times \text{Cost per foot}
\]

Substituting the values:

\[
\text{Cost of unused fencing} = 48 \times 12.60 = 604.80
\]

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

In conclusion, after constructing the garden, you have 48 feet of fencing left and the cost of the unused fencing amounts to $604.80.