Certainly! Let's find the length of the rectangular field given the information available.
### Step-by-Step Solution:
1. Identify the known values:
- Total amount of fencing available (Perimeter, [tex]\( P \)[/tex]): 260 meters
- Width of the rectangular field ([tex]\( W \)[/tex]): 50 meters
2. Understand the formula for the perimeter of a rectangle:
- The perimeter [tex]\( P \)[/tex] of a rectangle can be calculated using the formula:
[tex]\[
P = 2 \times (L + W)
\][/tex]
where [tex]\( L \)[/tex] is the length and [tex]\( W \)[/tex] is the width of the rectangle.
3. Substitute the known values into the perimeter formula:
- Plugging in the given perimeter and width:
[tex]\[
260 = 2 \times (L + 50)
\][/tex]
4. Solve for the length [tex]\( L \)[/tex]:
- First, simplify the equation:
[tex]\[
260 = 2L + 100
\][/tex]
- Subtract 100 from both sides:
[tex]\[
160 = 2L
\][/tex]
- Divide both sides by 2:
[tex]\[
L = 80
\][/tex]
### Conclusion:
The length of the rectangular field is 80 meters.
