1. **State the problem:** We need to find the actual area of Bedroom 1 from a scale drawing where 1 inch represents 3 feet. 2. **Given:** Bedroom 1 measures 3 1/2 inches by 3 1/2 inches on the drawing. 3. **Formula for actual length:** $$\text{Actual length} = \text{Drawing length} \times \text{Scale factor}$$ 4. **Calculate actual lengths:** Convert 3 1/2 inches to decimal: $$3 \frac{1}{2} = 3.5$$ inches. Actual length = $$3.5 \times 3 = 10.5$$ feet. Actual width = $$3.5 \times 3 = 10.5$$ feet. 5. **Formula for area:** $$\text{Area} = \text{length} \times \text{width}$$ 6. **Calculate actual area:** $$\text{Area} = 10.5 \times 10.5 = 110.25$$ square feet. 7. **Summary:** The actual area of Bedroom 1 is $$110.25$$ square feet. --- **Next problem:** Reproduce a scale drawing with a new scale 1 unit = 6 feet from an original scale 1 unit = 2 feet. 1. **State the problem:** Given a drawing with scale 1 unit = 2 feet, find the corresponding drawing with scale 1 unit = 6 feet. 2. **Formula for new drawing length:** $$\text{New drawing length} = \frac{\text{Actual length}}{\text{New scale factor}}$$ 3. **Example:** For a triangle with leg 4 units (original scale 2 feet/unit), actual length is: $$4 \times 2 = 8$$ feet. New drawing length: $$\frac{8}{6} = \frac{4}{3} \approx 1.33$$ units. 4. **Check all triangles:** - Triangle A (4,3) units original: - Actual legs: 8 ft, 6 ft - New drawing legs: $$\frac{8}{6} = 1.33$$, $$\frac{6}{6} = 1$$ units - Triangle B (2,1.5) units original: - Actual legs: 4 ft, 3 ft - New drawing legs: $$\frac{4}{6} = 0.67$$, $$\frac{3}{6} = 0.5$$ units - Triangle C (1,0.75) units original: - Actual legs: 2 ft, 1.5 ft - New drawing legs: $$\frac{2}{6} = 0.33$$, $$\frac{1.5}{6} = 0.25$$ units - Triangle D (6,4.5) units original: - Actual legs: 12 ft, 9 ft - New drawing legs: $$\frac{12}{6} = 2$$, $$\frac{9}{6} = 1.5$$ units 5. **Conclusion:** The drawing with legs approximately (1.33, 1) units corresponds to Triangle A scaled to 1 unit = 6 feet. --- **Final answers:** - Actual area of Bedroom 1: $$110.25$$ square feet. - New scale drawing lengths for Triangle A: approximately (1.33, 1) units.