1. **State the problem:** We need to find the hypotenuse $z$ of a right-angled triangle where the two legs are 3 cm and 6 cm. 2. **Formula:** Use Pythagoras' theorem which states: $$z^2 = a^2 + b^2$$ where $a$ and $b$ are the legs of the triangle. 3. **Substitute values:** $$z^2 = 3^2 + 6^2$$ $$z^2 = 9 + 36$$ $$z^2 = 45$$ 4. **Calculate $z$ by taking the square root:** $$z = \sqrt{45}$$ 5. **Simplify the square root:** $$z = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5}$$ 6. **Evaluate the decimal value:** $$z \approx 3 \times 2.236 = 6.708$$ 7. **Round to 1 decimal place:** $$z \approx 6.7$$ **Final answer:** $$z = 6.7 \text{ cm}$$