https://file.aiquickdraw.com/mathbot/file/1726013675724y1ok6f4d.jpg

In the image, you're asked to find the distance \( AB \) in a right-angled triangle, where:

- \( AD = 4 \, \text{cm} \)
- \( BC = 3 \, \text{cm} \)

From the diagram, we can infer that the triangle \( ABC \) forms a right triangle, and we can use the Pythagorean theorem to calculate the length of \( AB \). The Pythagorean theorem states:

\[
AB^2 = AD^2 + BC^2
\]

Substituting the given values:

\[
AB^2 = 4^2 + 3^2 = 16 + 9 = 25
\]

Thus, \( AB = \sqrt{25} = 5 \, \text{cm} \).

### Answer:
The distance \( AB \) is \( 5 \, \text{cm} \).

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Would you like further details or have any questions?

Here are five related questions to deepen your understanding:

1. How is the Pythagorean theorem applied in different types of triangles?
2. Can the Pythagorean theorem be used to find any other side of a right triangle?
3. What happens if one of the triangle's side lengths is missing or unknown?
4. How do we know that triangle \( ABC \) is a right triangle from the diagram?
5. What is the relationship between the sides of a triangle and the angles inside it?

**Tip**: Always check if a triangle is right-angled before applying the Pythagorean theorem.

Find the distance AB in the given diagram, where AD = 4 cm and BC = 3 cm.

Solve for the distance AB in a right-angled triangle where AD = 4 cm and BC = 3 cm. Learn how to apply the Pythagorean theorem and calculate the hypotenuse step by step. Suitable for middle school students.

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