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Part 1
A rectangular area is to be fenced in along a straight river bank as illustrated. The length of the​ fenced-in area is to be 6 feet greater than the​ width, and the total amount of fencing to be used is 66 feet. Find the width and length of the​ fenced-in area.
L
W




To solve this problem, we will first define the variables and set up equations based on the given information:

1. **Define the variables**:
   - Let \( W \) represent the width of the fenced-in area (in feet).
   - Let \( L \) represent the length of the fenced-in area (in feet).

2. **Set up the equations**:
   - According to the problem, the length \( L \) is 6 feet greater than the width \( W \). This can be written as:
     \[
     L = W + 6
     \]
   - The total amount of fencing to be used is 66 feet. Since the area is along a riverbank, fencing is needed on three sides: two widths and one length. Therefore, the total fencing used can be represented by:
     \[
     2W + L = 66
     \]

3. **Substitute the expression for \( L \) into the fencing equation**:
   - Substitute \( L = W + 6 \) into the equation \( 2W + L = 66 \):
     \[
     2W + (W + 6) = 66
     \]

4. **Solve for \( W \)**:
   - Combine like terms:
     \[
     3W + 6 = 66
     \]
   - Subtract 6 from both sides:
     \[
     3W = 60
     \]
   - Divide by 3:
     \[
     W = 20
     \]

5. **Find the length \( L \)**:
   - Substitute \( W = 20 \) back into the equation \( L = W + 6 \):
     \[
     L = 20 + 6 = 26
     \]

Thus, the width \( W \) of the fenced-in area is **20 feet**, and the length \( L \) is **26 feet**.

### Summary
- **Width (W)**: 20 feet
- **Length (L)**: 26 feet

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. What would the dimensions be if the total amount of fencing was 80 feet, with the same relationship between length and width?
2. How would the solution change if the fenced area was not along a river and required fencing on all four sides?
3. What would happen to the width and length if the length was instead 10 feet greater than the width?
4. How can you verify the solution using the perimeter formula for three sides?
5. What other methods could be used to solve this type of problem?

**Tip**: Always re-check your solutions by substituting back into the original equations to ensure consistency and correctness.

Learn how to calculate the width and length of a fenced area along a river bank using linear equations and perimeter formula. This problem involves setting up equations based on given dimensions and solving for unknowns. Suitable for students in Grades 6-8.

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