To determine the length of the dog run that Cindy can create with her 34 meters of fencing, we need to follow these steps:
1. Understand the given information:
- Total length of fencing available: 34 meters.
- Width of the dog run: 2 meters.
2. Recall the formula for the perimeter of a rectangle:
[tex]\[
P = 2L + 2W
\][/tex]
where [tex]\( P \)[/tex] is the perimeter, [tex]\( L \)[/tex] is the length, and [tex]\( W \)[/tex] is the width.
3. Substitute the given values into the perimeter formula:
- Let [tex]\( L \)[/tex] represent the length of the dog run.
- The perimeter [tex]\( P \)[/tex] is given as 34 meters.
- The width [tex]\( W \)[/tex] is given as 2 meters.
Substitute these values into the formula:
[tex]\[
34 = 2L + 2 \cdot 2
\][/tex]
4. Simplify the equation:
- First, multiply 2 by 2:
[tex]\[
2 \cdot 2 = 4
\][/tex]
- So the equation becomes:
[tex]\[
34 = 2L + 4
\][/tex]
5. Solve for the length [tex]\( L \)[/tex]:
- Subtract 4 from both sides to isolate the term with [tex]\( L \)[/tex]:
[tex]\[
34 - 4 = 2L
\][/tex]
- Simplify the left-hand side:
[tex]\[
30 = 2L
\][/tex]
- Divide both sides by 2 to solve for [tex]\( L \)[/tex]:
[tex]\[
L = \frac{30}{2}
\][/tex]
- Simplify the right-hand side:
[tex]\[
L = 15
\][/tex]
6. Conclusion:
- The length of the rectangular dog run that Cindy can create is 15 meters.
Therefore, the correct answer is 15 meters.
