1. **State the problem:** We need to find the greatest possible width of a rectangle whose area is more than 126 cm² and length is 18 cm. 2. **Formula:** The area $A$ of a rectangle is given by: $$A = \text{length} \times \text{width}$$ 3. **Given:** - Length $l = 18$ cm - Area $A > 126$ cm² 4. **Set up inequality:** $$18 \times w > 126$$ where $w$ is the width. 5. **Solve for $w$:** Divide both sides by 18: $$\cancel{18} \times w > \frac{126}{\cancel{18}}$$ $$w > 7$$ 6. **Interpretation:** The width must be greater than 7 cm to have an area more than 126 cm². 7. **Greatest possible value:** Since the width must be greater than 7, the greatest possible width is any value just greater than 7 cm. If the width must be an integer, the smallest integer greater than 7 is 8 cm. **Final answer:** The greatest possible width is any value greater than 7 cm.