1. **State the problem:** We are given a right triangle with legs measuring 4 cm and 5 cm. We need to find the length of the hypotenuse. 2. **Formula used:** In a right triangle, the Pythagorean theorem states that $$c^2 = a^2 + b^2$$ where $c$ is the hypotenuse and $a$, $b$ are the legs. 3. **Apply the formula:** Here, $a = 4$ cm and $b = 5$ cm. 4. Calculate $$c^2 = 4^2 + 5^2 = 16 + 25 = 41$$ 5. Find $c$ by taking the square root: $$c = \sqrt{41}$$ 6. **Answer:** The length of the hypotenuse is $\sqrt{41}$ cm. This corresponds to option C.