1. **State the problem:** We have a right triangle with legs measuring 6 cm and 8 cm. We need to find the length of the hypotenuse. 2. **Formula used:** In a right triangle, the Pythagorean theorem applies: $$c^2 = a^2 + b^2$$ where $c$ is the hypotenuse and $a$, $b$ are the legs. 3. **Apply the formula:** Substitute $a=6$ and $b=8$: $$c^2 = 6^2 + 8^2$$ 4. **Calculate squares:** $$c^2 = 36 + 64$$ 5. **Sum the squares:** $$c^2 = 100$$ 6. **Find the hypotenuse by taking the square root:** $$c = \sqrt{100}$$ 7. **Simplify the square root:** $$c = 10$$ **Final answer:** The length of the hypotenuse is 10 cm.