A school room is to be built to accommodate 70 children so as to allow 2.2 m² of floor and 11 m³ of space for each child. If the room be 14 metres long, what must be its breadth and height?

### Concept & Intersecting Constraints The room is governed by two constraints: floor area (which dictates breadth since length is fixed) and total volume (which dictates height once the floor area is known). $$ Total Area = Number of Children \times Area per Child $$ $$ Total Volume = Number of Children \times Volume per Child $$ ### Step-by-Step Solution 1. **Find Total Floor Area & Determine Breadth**: - Total Area required = $70 \times 2.2 = 154$ m² - We know $Area = Length \times Breadth$ - $154 = 14 \times Breadth$ - $Breadth = \frac{154}{14} = 11$ m 2. **Find Total Volume & Determine Height**: - Total Volume required = $70 \times 11 = 770$ m³ - We know $Volume = Area \times Height$ - $770 = 154 \times Height$ - $Height = \frac{770}{154} = 5$ m ### Exam Strategy & Shortcut There is a direct relationship between Volume, Area, and Height. Since $Volume = Area \times Height$, the height of the room is simply the ratio of Volume per child to Area per child. $Height = \frac{11 \text{ m}^3}{2.2 \text{ m}^2} = 5 \text{ m}$. Looking at the options, only (b) has a height of 5 m, so you can choose it instantly without even calculating the breadth! ### Common Pitfall Unnecessarily calculating the total volume (770) and total area (154) just to find height, rather than realizing height applies uniformly per child. ### Final Answer Therefore, the correct answer is **11 m, 5 m**.