House Plan Ea427D

1. **State the problem:** We have a rectangular house plan with several rooms and areas given or partially given. We need to find the missing dimensions and the total area of the house. 2. **Given data:** - Master Bedroom: $15 \text{ ft} \times 15 \text{ ft}$, Area = $225 \text{ sq ft}$ - Toilet: $5 \text{ ft} \times 10 \text{ ft}$ - Utility: dimensions unknown, area unknown - Kitchen: $15 \text{ ft} \times 12 \text{ ft}$, Area = $180 \text{ sq ft}$ - Small Bedroom: $15 \text{ ft} \times x \text{ ft}$, Area = $180 \text{ sq ft}$ - Hall: area unknown - Garden: dimensions and area unknown - Parking: dimensions and area unknown 3. **Find missing dimension of Small Bedroom:** Formula for area of rectangle: $$\text{Area} = \text{length} \times \text{width}$$ Given area = $180$ sq ft and length = $15$ ft, $$180 = 15 \times x$$ Divide both sides by 15: $$\cancel{15} \times x = \frac{180}{\cancel{15}}$$ $$x = 12$$ So, Small Bedroom dimensions are $15 \text{ ft} \times 12 \text{ ft}$. 4. **Find Utility dimensions:** From the layout, Utility is above Kitchen and next to Toilet. Since Kitchen width is $12$ ft and Toilet width is $5$ ft, total width of Utility + Toilet = $15$ ft (same as Master Bedroom length). Utility width = $15 - 5 = 10$ ft. Utility length is unknown; assume it equals Toilet length $10$ ft (common in plans). Area of Utility = $10 \text{ ft} \times 10 \text{ ft} = 100$ sq ft. 5. **Find Hall area and dimensions:** Assuming the house is a rectangle with length $30$ ft (sum of Master Bedroom $15$ ft + Small Bedroom $15$ ft) and width $27$ ft (sum of Kitchen $12$ ft + Utility $10$ ft + Toilet $5$ ft), total house area is: $$30 \times 27 = 810 \text{ sq ft}$$ Sum of known room areas: Master Bedroom: $225$ sq ft Small Bedroom: $180$ sq ft Kitchen: $180$ sq ft Utility: $100$ sq ft Toilet: $5 \times 10 = 50$ sq ft Sum = $225 + 180 + 180 + 100 + 50 = 735$ sq ft Remaining area for Hall, Garden, Parking: $$810 - 735 = 75 \text{ sq ft}$$ 6. **Find Garden and Parking dimensions and areas:** Assuming Garden and Parking are strips along the bottom, their combined area is $75$ sq ft. If Garden width = $15$ ft and Parking width = $15$ ft (matching room widths), and length $x$ ft, Total length $x$ satisfies: $$15x + 15x = 75$$ $$30x = 75$$ Divide both sides by 30: $$\cancel{30}x = \frac{75}{\cancel{30}}$$ $$x = 2.5$$ So Garden and Parking each have length $2.5$ ft. Garden area = $15 \times 2.5 = 37.5$ sq ft Parking area = $15 \times 2.5 = 37.5$ sq ft 7. **Summary of missing measurements:** - Small Bedroom width = $12$ ft - Utility dimensions = $10$ ft by $10$ ft - Garden dimensions = $15$ ft by $2.5$ ft - Parking dimensions = $15$ ft by $2.5$ ft - Hall area = $0$ sq ft (assumed zero or included in other spaces) 8. **Total area of the house:** $$810 \text{ sq ft}$$ This matches the sum of all rooms and spaces. **Final answers:** - Small Bedroom width = $12$ ft - Utility = $10$ ft by $10$ ft - Garden = $15$ ft by $2.5$ ft - Parking = $15$ ft by $2.5$ ft - Total house area = $810$ sq ft