Question 2

A man has [tex][tex]$260 \, \text{m}$[/tex][/tex] of fencing which he is going to put around a rectangular field that is [tex][tex]$50 \, \text{m}$[/tex][/tex] wide. How long is the field?



Answer :

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.