1. **Problem Statement:** We are given a scale of 1:500000 and a drawn length of 15 cm. We need to find the actual length represented by this drawn length. 2. **Understanding the Scale:** A scale of 1:500000 means that 1 unit on the drawing corresponds to 500000 units in reality. 3. **Formula:** $$\text{Actual length} = \text{Drawn length} \times \text{Scale factor}$$ 4. **Calculation:** Given drawn length = 15 cm $$\text{Actual length} = 15 \text{ cm} \times 500000 = 7500000 \text{ cm}$$ 5. **Convert to meters:** Since 100 cm = 1 m, $$7500000 \text{ cm} = \frac{7500000}{100} = 75000 \text{ m}$$ 6. **Answer for (a):** The actual length is 75000 meters. --- 7. **Problem (b) Statement:** On a scale diagram of 1:50, find the drawn length if the actual length is 12 m. 8. **Understanding the Scale:** Scale 1:50 means 1 unit on the drawing corresponds to 50 units in reality. 9. **Formula:** $$\text{Drawn length} = \frac{\text{Actual length}}{\text{Scale factor}}$$ 10. **Calculation:** Actual length = 12 m = 1200 cm (since 1 m = 100 cm) $$\text{Drawn length} = \frac{1200 \text{ cm}}{50} = 24 \text{ cm}$$ 11. **Answer for (b):** The drawn length is 24 cm. --- 12. **Additional Scale Conversions:** - 4 cm represents 5 m means scale is 1:125 (since 4 cm on drawing = 500 cm actual, so 1 cm = 125 cm) - 5 cm represents 4 km means scale is 1:80000 (since 5 cm = 400000 cm, so 1 cm = 80000 cm) - 1 cm represents 1 m means scale is 1:100 (since 1 cm = 100 cm) These help understand different scale ratios. **Final answers:** (a) Actual length = 75000 m (b) Drawn length = 24 cm