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The problem involves a right triangle where a farmer builds three sections of a fence. The given value for \( L \) is \( 20.00 \, \text{m} \), and the diagram shows a right triangle with legs \( L \) and \( \frac{L}{2} \). The goal is to determine the distance \( d \), which is the hypotenuse, that the farmer would need to walk to return to his starting point.

### Steps to Solve:
1. **Identify the sides of the triangle:**
   - One leg of the triangle \( L = 20.00 \, \text{m} \).
   - The other leg is \( \frac{L}{2} = \frac{20.00}{2} = 10.00 \, \text{m} \).

2. **Use the Pythagorean theorem** to find \( d \):
   \[
   d = \sqrt{L^2 + \left(\frac{L}{2}\right)^2}
   \]
   Substitute the given values:
   \[
   d = \sqrt{(20.00)^2 + (10.00)^2}
   \]
   \[
   d = \sqrt{400 + 100} = \sqrt{500} \approx 22.36 \, \text{m}
   \]

### Conclusion:
The correct distance \( d \) that the farmer would have to walk back is approximately \( 22.36 \, \text{m} \).

Would you like more details, or do you have any further questions?

Here are five related questions:
1. What is the importance of the Pythagorean theorem in real-world applications?
2. How do you calculate the length of the hypotenuse in a right triangle if the lengths of the legs are known?
3. What happens to the hypotenuse if both legs of a right triangle are doubled?
4. Can the Pythagorean theorem be applied to non-right triangles? If so, how?
5. What are the implications of the Pythagorean theorem in construction and design?

**Tip:** When solving problems involving the Pythagorean theorem, always ensure that the triangle is right-angled before applying the theorem.

A farmer builds three sections of a fence, as shown in the figure, where L = 20.00 m, and gets tired. Walking straight back to where he started, how far did he have to go?

This problem involves calculating the distance a farmer must walk back to his starting point using the Pythagorean theorem. Given the lengths L = 20.00 m and L/2 = 10.00 m, the distance d is approximately 22.36 m. Suitable for students in Grades 8-10.

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