1. **Problem 1: Find the actual length of the patio.** The scale is 1 centimeter = 0.5 meter. Let $x$ be the actual length in meters. We write the proportion: $$\frac{1 \text{ cm}}{0.5 \text{ m}} = \frac{4.5 \text{ cm}}{x \text{ m}}$$ 2. Cross multiply: $$1 \cdot x = 0.5 \cdot 4.5$$ 3. Calculate the right side: $$x = 2.25$$ **Answer:** The actual length of the patio is 2.25 meters. 4. **Problem 2: Find the corresponding distance on the drawing for 11.2 meters actual distance.** Let $d$ be the drawing distance in centimeters. Write the proportion: $$\frac{1 \text{ cm}}{0.5 \text{ m}} = \frac{d \text{ cm}}{11.2 \text{ m}}$$ 5. Cross multiply: $$1 \cdot 11.2 = 0.5 \cdot d$$ 6. Solve for $d$: $$11.2 = 0.5 d$$ Divide both sides by 0.5: $$\cancel{0.5} d = \frac{11.2}{\cancel{0.5}}$$ $$d = 22.4$$ **Answer:** The corresponding distance on the drawing is 22.4 centimeters. 7. **Problem 3: Find the scale factor for the drawing.** The scale is 1 cm = 0.5 m. Convert 0.5 meters to centimeters: $$0.5 \text{ m} = 0.5 \times 100 = 50 \text{ cm}$$ 8. Write the ratio in simplest form: $$\frac{1 \text{ cm}}{50 \text{ cm}} = \frac{1}{50}$$ **Answer:** The scale factor is $\frac{1}{50}$ or 1:50, meaning each distance on the drawing is 1/50 of the actual distance.