This is a right triangle problem, and we are asked to find the length of the hypotenuse $AC$.

Given:

• Side $AB = 5$ (one leg),
• Side $BC = 12$ (the other leg).

We can use the Pythagorean theorem to find the hypotenuse $AC$. The theorem is:

$AC^2 = AB^2 + BC^2$

Substitute the values:

$AC^2 = 5^2 + 12^2 = 25 + 144 = 169$

$AC = \sqrt{169} = 13$

Thus, the length of the hypotenuse $AC$ is 13.

Would you like further details or have any questions?

Here are 5 questions to expand on this:

1. What is the Pythagorean theorem used for in general?
2. How can you determine if a triangle is a right triangle using side lengths?
3. Can the Pythagorean theorem be applied to non-right triangles?
4. How would the problem change if the triangle was not a right triangle?
5. What are other methods to find the hypotenuse besides the Pythagorean theorem?

Tip: Always double-check if a triangle is a right triangle before using the Pythagorean theorem, as it only applies to right-angled triangles.