1. **Problem:** Given the scale 1.5 inches = 2 feet, find the actual lengths of each room from their drawing lengths. 2. **Formula:** Use the scale factor to convert drawing length to actual length: $$\text{Actual Length} = \frac{2}{1.5} \times \text{Drawing Length}$$ 3. **Calculate scale factor:** $$\text{Scale factor} = \frac{2}{1.5} = \frac{4}{3} \approx 1.3333$$ 4. **Calculate actual lengths:** - Living Room: $$15 \times \frac{4}{3} = 20 \text{ feet}$$ - Dining Room: $$10.5 \times \frac{4}{3} = 14 \text{ feet}$$ - Kitchen: Convert mixed number $$12 \frac{3}{4} = 12.75$$ $$12.75 \times \frac{4}{3} = 17 \text{ feet}$$ - Laundry Room: Convert mixed number $$8 \frac{1}{4} = 8.25$$ $$8.25 \times \frac{4}{3} = 11 \text{ feet}$$ - Hall: Convert mixed number $$13 \frac{7}{8} = 13.875$$ $$13.875 \times \frac{4}{3} = 18.5 \text{ feet}$$ - Garage: $$16.5 \times \frac{4}{3} = 22 \text{ feet}$$ 5. **Answer for question 7:** The scale factor of these drawings is $$\frac{4}{3}$$ or approximately 1.3333. --- 6. **Town Planning scale:** 1 inch = 7 feet. 7. **Question 8:** Courthouse height in model = $$5 \frac{1}{2} = 5.5$$ inches. Actual height: $$5.5 \times 7 = 38.5 \text{ feet}$$ 8. **Question 9:** Lamppost actual height = 12 feet. Model height: $$\frac{12}{7} = \frac{12}{7} \approx 1.714 \text{ inches}$$ 9. **Question 10:** Lampposts distance in model = $$3 \frac{3}{7} = \frac{24}{7} \approx 3.4286$$ inches. Actual distance: $$3.4286 \times 7 = 24 \text{ feet}$$ 10. **Question 11:** Scale factor is $$7$$ (feet per inch). --- 11. **Question 12:** Map distance = $$6 \frac{1}{2} = 6.5$$ inches. Actual distance = 104 miles. Scale: $$\text{Scale} = \frac{104}{6.5} = 16 \text{ miles per inch}$$ **Final answers:** - Living Room: 20 feet - Dining Room: 14 feet - Kitchen: 17 feet - Laundry Room: 11 feet - Hall: 18.5 feet - Garage: 22 feet - Scale factor (architecture): $$\frac{4}{3}$$ - Courthouse height: 38.5 feet - Lamppost model height: 1.714 inches - Lamppost actual distance: 24 feet - Scale factor (town planning): 7 - Map scale: 16 miles per inch