1. **Problem statement:** Find the length of the unknown side in the first problem (a right triangle with one leg 6 cm and unknown hypotenuse). 2. **Formula used:** In a right triangle, the Pythagorean theorem applies: $$c = \sqrt{a^2 + b^2}$$ where $c$ is the hypotenuse and $a$, $b$ are the legs. 3. **Given:** One leg $a = 6$ cm, the other leg is unknown or zero, so we assume the other leg is 0 or the problem implies the hypotenuse is unknown with one leg 6 cm. 4. Since only one leg is given and the hypotenuse is unknown, we need the other leg to calculate the hypotenuse. Assuming the other leg is the same as the first leg (since no other info), then: $$c = \sqrt{6^2 + 6^2} = \sqrt{36 + 36} = \sqrt{72}$$ 5. Simplify: $$\sqrt{72} = \sqrt{36 \times 2} = 6\sqrt{2} \approx 8.485$$ 6. Rounded to the nearest mm (0.1 cm): $$c \approx 8.5 \text{ cm}$$ **Final answer:** The length of the unknown hypotenuse is approximately **8.5 cm**.