1. **Problem statement:** Calculate the length of segment AB in a rectangular prism where the edges from vertex A are 2 cm, 5 cm, and 9 cm long. 2. **Formula used:** To find the length of the diagonal AB in a rectangular prism, use the 3D distance formula derived from the Pythagorean theorem: $$AB = \sqrt{a^2 + b^2 + c^2}$$ where $a$, $b$, and $c$ are the lengths of the edges meeting at vertex A. 3. **Apply the values:** Here, $a=2$, $b=5$, and $c=9$. $$AB = \sqrt{2^2 + 5^2 + 9^2}$$ 4. **Calculate squares:** $$AB = \sqrt{4 + 25 + 81}$$ 5. **Sum inside the square root:** $$AB = \sqrt{110}$$ 6. **Calculate the square root:** $$AB \approx 10.4881$$ 7. **Round to 1 decimal place:** $$AB \approx 10.5$$ **Final answer:** The length of AB is approximately **10.5 cm**.