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The problem asks for the length of the line segment \( AB \) in the given figure, where there are a series of connected right triangles, each with leg lengths of \( 1 \) meter.

### Solution:
1. Since each triangle in the figure is a right triangle with one leg of \( 1 \) meter, we can use the Pythagorean theorem to calculate the hypotenuse of each triangle.
   
2. For each right triangle, with legs of \( 1 \) meter and \( 1 \) meter:
   \[
   \text{Hypotenuse} = \sqrt{1^2 + 1^2} = \sqrt{2}
   \]

3. Moving from point \( B \) to point \( A \), there are three right triangles that are connected. Each hypotenuse contributes a length of \( \sqrt{2} \) meters along the segment \( AB \).

4. Therefore, the total length of \( AB \) is:
   \[
   AB = 3 \times \sqrt{2} = 3\sqrt{2} \text{ meters}
   \]

### Final Answer:
\[
AB = 3\sqrt{2} \text{ meters}
\]

Would you like a more detailed explanation of the steps or have any questions?

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### Related Questions:
1. How do you calculate the hypotenuse of a right triangle with legs of different lengths?
2. What is the Pythagorean theorem, and how is it used in geometry?
3. If each triangle had legs of \( 2 \) meters, how would the length of \( AB \) change?
4. How can the length \( 3\sqrt{2} \) be approximated as a decimal?
5. How do geometric series apply to similar right triangles?

### Tip:
When dealing with right triangles, always check if you can simplify the expression using the Pythagorean theorem, especially in figures with repeated geometric patterns like this one.

Find the length of line segment AB in the given figure where each triangle has legs of 1 meter.

Learn how to find the length of line segment AB in a sequence of right triangles with 1-meter legs using the Pythagorean theorem. Suitable for students in Grades 8-10, this solution provides a step-by-step approach to solving geometric problems with repeated patterns.

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