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.