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The floor of a rectangular room of 72 square meters area needs to be covered by a circular carpet that occupies exactly half the area of the floor. What must be the circumference of the carpet in meters?
  • a)
    3√π
  • b)
    6√π
  • c)
    9√π
  • d)
    12√π
  • e)
    15√π
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The floor of a rectangular room of 72 square meters area needs to be c...
Given that the area of the rectangular floor = 72 square meters
And that the carpet occupies exactly half the area.
Area of carpet = 36 square meters.
Let the radius of carpet = R meters
Therefore πR2 = 36
Therefore the circumference  = 
 meters
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Most Upvoted Answer
The floor of a rectangular room of 72 square meters area needs to be c...
To solve this problem, we need to find the circumference of the circular carpet that occupies exactly half the area of the rectangular room.

Let's assume the length and width of the rectangular room are L and W respectively. We are given that the area of the rectangular room is 72 square meters.

1. Determine the area of the circular carpet:
Since the circular carpet occupies exactly half the area of the rectangular room, the area of the circular carpet is half of the area of the rectangular room.
Area of the rectangular room = L * W = 72 square meters
Area of the circular carpet = 72 / 2 = 36 square meters

2. Calculate the radius of the circular carpet:
The area of a circle is given by the formula A = π * r^2, where A is the area and r is the radius.
36 = π * r^2
r^2 = 36 / π
r^2 ≈ 11.46
r ≈ √11.46 ≈ 3.39 meters

3. Find the circumference of the circular carpet:
The circumference of a circle is given by the formula C = 2 * π * r, where C is the circumference and r is the radius.
C = 2 * π * 3.39 ≈ 21.3 meters

Therefore, the circumference of the circular carpet is approximately 21.3 meters.

The correct answer is option D) 12.
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