1. The problem is to find the length of the hypotenuse $c$ of a right triangle with legs measuring 6 cm and 8 cm. 2. We use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse $c$ is equal to the sum of the squares of the other two sides $a$ and $b$: $$c^2 = a^2 + b^2$$ 3. Substitute the given values $a = 6$ cm and $b = 8$ cm: $$c^2 = 6^2 + 8^2$$ 4. Calculate the squares: $$c^2 = 36 + 64$$ 5. Add the results: $$c^2 = 100$$ 6. To find $c$, take the square root of both sides: $$c = \sqrt{100}$$ 7. Simplify the square root: $$c = 10$$ 8. Therefore, the length of the hypotenuse $c$ is 10 centimetres.