1. **Problem statement:** We need to find the length of side $FG$ in a right triangle $FGH$ where the right angle is at vertex $F$. The sides $FH$ and $HG$ are given as 6 cm and 15 cm respectively. 2. **Formula used:** In a right triangle, by the Pythagorean theorem, the length of the hypotenuse $FG$ is given by: $$FG = \sqrt{FH^2 + HG^2}$$ 3. **Substitute the known values:** $$FG = \sqrt{6^2 + 15^2}$$ 4. **Calculate the squares:** $$FG = \sqrt{36 + 225}$$ 5. **Add the values inside the square root:** $$FG = \sqrt{261}$$ 6. **Calculate the square root:** $$FG \approx 16.1554944214$$ 7. **Round to 1 decimal place:** $$FG \approx 16.2$$ **Final answer:** The length of $FG$ is approximately 16.2 cm.