1. **Problem statement:** We need to find the length of the diagonal $DG$ inside the cuboid. 2. **Given dimensions:** - Height $EH = 24$ cm - Length $EF = 41$ cm - Width $FB = 22$ cm 3. **Understanding the cuboid:** - The cuboid has edges along three perpendicular directions: height, length, and width. - The diagonal $DG$ runs from one bottom corner $D$ to the opposite top corner $G$. 4. **Formula for the space diagonal of a cuboid:** $$DG = \sqrt{(length)^2 + (width)^2 + (height)^2}$$ 5. **Substitute the values:** $$DG = \sqrt{41^2 + 22^2 + 24^2}$$ 6. **Calculate each square:** $$41^2 = 1681$$ $$22^2 = 484$$ $$24^2 = 576$$ 7. **Sum the squares:** $$1681 + 484 + 576 = 2741$$ 8. **Calculate the square root:** $$DG = \sqrt{2741} \approx 52.35$$ 9. **Round to 1 decimal place:** $$DG \approx 52.4$$ cm **Final answer:** The length of diagonal $DG$ is approximately **52.4 cm**.