1. **Stating the problem:** We are given a scale where 1 cm represents 20 m, and we need to write the scale as a ratio and find the scale factor. 2. **Writing the scale as a ratio:** The scale ratio compares the length on the diagram to the actual length in the same units. Given 1 cm represents 20 m, convert 20 m to cm: $$20\text{ m} = 20 \times 100 = 2000\text{ cm}$$ So the scale ratio is $$1\text{ cm} : 2000\text{ cm}$$ or simplified as $$1:2000$$. 3. **Finding the scale factor:** The scale factor is the ratio of the drawing length to the actual length, which is $$\frac{1}{2000}$$. 4. **Writing other scales as ratios:** - For 1 cm represents 10 m: Convert 10 m to cm: $$10 \times 100 = 1000\text{ cm}$$ Scale ratio: $$1:1000$$. - For 1 cm represents 50 km: Convert 50 km to cm: $$50\text{ km} = 50 \times 1000 \times 100 = 5,000,000\text{ cm}$$ Scale ratio: $$1:5,000,000$$. 5. **Finding the drawn length of an object 12 m long with scale 1:100:** Scale 1:100 means 1 cm on drawing represents 100 cm (or 1 m) in reality. Convert 12 m to cm: $$12 \times 100 = 1200\text{ cm}$$ Drawn length = $$\frac{1200}{100} = 12\text{ cm}$$. **Final answers:** - a) Scale ratio for 1 cm represents 20 m is $$1:2000$$. - b) Scale factor is $$\frac{1}{2000}$$. - 1 cm represents 10 m scale ratio: $$1:1000$$. - 1 cm represents 50 km scale ratio: $$1:5,000,000$$. - Drawn length of 12 m object at 1:100 scale is $$12\text{ cm}$$.