1. **State the problem:** We need to find the length of the train in the scale diagram given the real length and the scale ratio. 2. **Given:** The scale ratio is 1 : 200, meaning 1 unit on the diagram represents 200 units in real life. 3. **Real length of the train:** 90 meters. 4. **Convert real length to the same unit as the diagram:** Since the diagram length is asked in centimetres, convert 90 meters to centimetres. $$90 \text{ m} = 90 \times 100 = 9000 \text{ cm}$$ 5. **Use the scale ratio to find the diagram length:** $$\text{Diagram length} = \frac{\text{Real length}}{\text{Scale factor}} = \frac{9000}{200} = 45 \text{ cm}$$ 6. **Answer:** The length of the train in the diagram is **45 centimetres**.