The length, breadth and height of a room are 1, b and h respectively. The perimeter of the ceiling expressed as a percentage of the total area of the four walls is
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UPSC Civil Services preparation
- A100 h
- B100/hCorrect
- Ch
- Dh/100
Explanation
To find the correct answer, we use the formulas for the perimeter of the ceiling and the area of the four walls.
1. The perimeter of the ceiling of a room with length l and breadth b is 2 multiplied by the sum of l and b. Formula: 2(l + b).
2. The total area of the four walls is the perimeter of the floor multiplied by the height h. Formula: 2(l + b)h.
3. To express the perimeter as a percentage of the total area of the four walls, we divide the perimeter by the area and multiply by 100.
Calculation:
Percentage = (Perimeter / Area of four walls) multiplied by 100
Percentage = (2(l + b) / 2(l + b)h) multiplied by 100
The term 2(l + b) cancels out from the numerator and the denominator, leaving:
Percentage = (1 / h) multiplied by 100
Percentage = 100/h
Therefore, the correct option is B.
