1. **Problem statement:** We need to find the length of side $QR$ in right triangle $PQR$ where the right angle is at vertex $P$. Given sides are $PQ = 8$ cm and $PR = 3$ cm. 2. **Formula used:** In a right triangle, the Pythagorean theorem applies: $$QR^2 = PQ^2 + PR^2$$ This means the square of the hypotenuse ($QR$) equals the sum of the squares of the other two sides. 3. **Calculate squares:** $$PQ^2 = 8^2 = 64$$ $$PR^2 = 3^2 = 9$$ 4. **Sum the squares:** $$QR^2 = 64 + 9 = 73$$ 5. **Find $QR$ by taking the square root:** $$QR = \sqrt{73}$$ 6. **Approximate the square root:** $$QR \approx 8.544\ldots$$ 7. **Round to 1 decimal place:** $$QR \approx 8.5$$ **Final answer:** The length of $QR$ is approximately 8.5 cm.