1. **State the problem:** We need to find the length of the hypotenuse $QR$ in a right triangle $PQR$ where the right angle is at $P$. The sides adjacent to the right angle are $PQ = 8$ cm and $PR = 3$ cm. 2. **Formula used:** In a right triangle, the Pythagorean theorem states: $$QR^2 = PQ^2 + PR^2$$ This means the square of the hypotenuse equals the sum of the squares of the other two sides. 3. **Calculate the squares:** $$PQ^2 = 8^2 = 64$$ $$PR^2 = 3^2 = 9$$ 4. **Sum the squares:** $$QR^2 = 64 + 9 = 73$$ 5. **Find the length of $QR$ by taking the square root:** $$QR = \sqrt{73}$$ 6. **Approximate the square root to 1 decimal place:** $$QR \approx 8.5$$ **Final answer:** The length of $QR$ is approximately **8.5 cm**.