Given that triangle $\Delta ABC$ is a right triangle with the right angle at $B$, and the lengths of the sides $AB = 3 \, \text{cm}$ and $BC = 4 \, \text{cm}$, we can use the Pythagorean theorem to find the length of the hypotenuse $AC$.

The Pythagorean theorem states:

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

Substituting the known values:

$AC^2 = 3^2 + 4^2$ $AC^2 = 9 + 16$ $AC^2 = 25$ $AC = \sqrt{25}$ $AC = 5 \, \text{cm}$

Therefore, the length of $AC$ is 5 cm.

Would you like further details or have any questions? Here's a list of related questions for your reference:

1. How do you verify the Pythagorean theorem for other right-angled triangles?
2. What happens if one of the sides of the right triangle is unknown?
3. How does the Pythagorean theorem extend to 3-dimensional space?
4. Can the Pythagorean theorem be used for non-right-angled triangles?
5. How do you calculate the perimeter and area of a right-angled triangle?

Tip: Always double-check the given side lengths when using the Pythagorean theorem to avoid errors in calculation!