The problem involves a thin wire of 18 cm that has been bent into an "L" shape, forming two segments of 3 cm each on the legs of a right-angled triangle, with points A and B as shown. We are asked to calculate the length of the segment from point A to point B, which forms the hypotenuse of the right triangle.

Step-by-Step Solution:

1. Identify the segments:

   • The two legs of the right triangle are both 3 cm in length.

2. Use the Pythagorean theorem: The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides:

   $AB^2 = 3^2 + 3^2$

   Simplifying:

   $AB^2 = 9 + 9 = 18$

3. Solve for AB:

   $AB = \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2} \approx 4.24 \text{ cm}$

Therefore, the length of the segment from point A to point B is approximately 4.24 cm.

Would you like more details or have any questions?

Related questions:

1. How would the length change if the wire had different leg lengths?
2. Can you apply the Pythagorean theorem in other geometric configurations?
3. How can you determine the length of a wire if it's bent into different shapes?
4. What if the wire was longer than 18 cm—how would that affect the triangle?
5. What is the relation between wire length and the shape formed?

Tip: When solving right triangle problems, always check if the Pythagorean theorem applies, as it is a fundamental tool for determining unknown sides.