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.