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This problem asks to calculate the straight-line distance \( d \) the farmer has to walk back to the starting point, as shown in the diagram. The diagram forms a right triangle, where:

- One leg is the total height, \( L + L = 2L = 20.00 \, \text{m} \),
- The other leg is \( L/2 = 10.00 / 2 = 5.00 \, \text{m} \).

We can use the Pythagorean theorem to calculate the hypotenuse \( d \), which is the straight-line distance:

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

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

\[
d = \sqrt{(20.00)^2 + (5.00)^2}
\]

Let me calculate this.The straight-line distance \( d \) that the farmer has to walk back to the starting point is approximately \( 20.62 \, \text{m} \).

Would you like more details on the calculation, or do you have any other questions?

Here are 5 related questions to expand on the topic:
1. How does the Pythagorean theorem work for calculating distances in right triangles?
2. What if the lengths of the fence sections were different—how would you calculate \( d \) then?
3. How would the formula change if the ground wasn't flat (e.g., there was a slope)?
4. Could we use trigonometry to solve this problem in a different way?
5. What if the farmer had built four sections of fence instead of three?

**Tip:** For right triangles, the Pythagorean theorem \( a^2 + b^2 = c^2 \) is a useful tool to find the hypotenuse or any missing side when the other two sides are known.

A farmer builds three sections of a fence, where L = 10.00 m. Walking straight back to the start, how far did he have to go?

Learn how to calculate the straight-line distance (d) a farmer must walk back to the starting point after building three sections of a fence using the Pythagorean theorem. Given L = 10.00 m, we find that the farmer walks approximately 20.62 m. Suitable for students in Grades 7-9.

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