1. **State the problem:** We need to find the maximum force that can be safely applied to a rectangular floor tile given its dimensions and the maximum pressure it can sustain. 2. **Given data:** - Length of tile $= 2.3$ m (to nearest 0.1 m) - Width of tile $= 1.6$ m (to nearest 0.1 m) - Maximum pressure $= 200$ N/m$^2$ (to nearest 5 N/m$^2$) 3. **Formula:** Pressure $= \frac{\text{Force}}{\text{Area}}$ 4. **Calculate the area of the tile:** $$\text{Area} = \text{Length} \times \text{Width} = 2.3 \times 1.6 = 3.68 \text{ m}^2$$ 5. **Calculate the maximum force:** Rearranging the formula for force, $$\text{Force} = \text{Pressure} \times \text{Area}$$ Substitute the values, $$\text{Force} = 200 \times 3.68 = 736 \text{ N}$$ 6. **Interpretation:** The maximum force that can safely be applied to the tile is approximately 736 Newtons. 7. **Note on rounding:** The problem states the pressure is correct to the nearest 5 N/m$^2$, so the force is also approximate. **Final answer:** $$\boxed{736 \text{ N}}$$