1. **State the problem:** We are given the length of a building on a plan as 22.5 cm and the actual length of the building as 29.25 m. We need to find the scale of the plan as a simplified ratio. 2. **Convert units:** Since the plan length is in centimeters and the actual length is in meters, convert the actual length to centimeters for consistency. $$29.25\text{ m} = 29.25 \times 100 = 2925 \text{ cm}$$ 3. **Write the scale ratio:** The scale is the ratio of the plan length to the actual length. $$\text{Scale} = \frac{22.5 \text{ cm}}{2925 \text{ cm}}$$ 4. **Simplify the ratio:** Divide numerator and denominator by 22.5. $$\frac{\cancel{22.5}}{\cancel{22.5}} : \frac{2925}{22.5} = 1 : \frac{2925}{22.5}$$ Calculate the denominator: $$\frac{2925}{22.5} = 130$$ 5. **Final scale:** $$\boxed{1 : 130}$$ This means 1 cm on the plan represents 130 cm (or 1.3 m) in reality.