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This problem involves calculating the straight-line distance \( d \) the farmer needs to walk to return to the starting point after building the fence sections.

From the diagram, we observe that the three sections form a right triangle. The fence sections have lengths:
- Two sides of length \( L = 10.00 \, \text{m} \),
- One horizontal side of length \( L/2 = 5.00 \, \text{m} \).

To find the straight-line distance \( d \), we can use the Pythagorean theorem since the path forms a right triangle:

\[
d = \sqrt{(L)^2 + \left(\frac{L}{2}\right)^2}
\]

Substituting \( L = 10.00 \, \text{m} \):

\[
d = \sqrt{(10.00)^2 + \left(\frac{10.00}{2}\right)^2}
= \sqrt{100.00 + 25.00}
= \sqrt{125.00}
\]

\[
d = 11.18 \, \text{m}
\]

Thus, the farmer needs to walk \( d = 11.18 \, \text{m} \).

Would you like further details on this? Here are five related questions to explore:

1. How would the value of \( d \) change if \( L \) were doubled?
2. Can the Pythagorean theorem be applied to any triangle, or just right triangles?
3. What happens to the value of \( d \) if the farmer builds only two sections instead of three?
4. How can we verify this result geometrically or experimentally?
5. How would this problem change if the farmer walked along a curved path instead of straight sections?

**Tip:** Whenever solving problems involving right triangles, the Pythagorean theorem is a powerful tool to find unknown sides!

A farmer builds three sections of a fence, as shown in the figure, where L = 10.00 m, and gets tired. Walking straight back to where he started, how far d did he have to go?

This problem involves using the Pythagorean theorem to calculate the straight-line distance a farmer needs to walk after building three fence sections. Given L = 10.00 m, learn how to apply the theorem to find d.

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