State 'T' for true and 'F' for false.
(i) The perimeter of a regular hexagon of side 2 m is 12 m.
(ii) If the side of a square floor is 9 m, then the area of the carpet needed to cover the floor of the room is `36 m^(2)`.
(iii) A square and rectangle can have same perimeter.

Options

A. `{:(i,ii,iii,),(T,F,T,):}`
B. `{:(i,ii,iii,),(F,T,F,):}`
C. `{:(i,ii,iii,),(F,T,T,):}`
D. `{:(i,ii,iii,),(F,F,T,):}`

Answer

Let's solve the question step by step.

### Step 1: Determine the perimeter of a regular hexagon with a side of 2 m.
- A regular hexagon has 6 equal sides.
- The formula for the perimeter (P) of a hexagon is:
\[ P = 6 \times \text{side} \]
- Substituting the given side length:
\[ P = 6 \times 2 \, \text{m} = 12 \, \text{m} \]
- Therefore, the statement "The perimeter of a regular hexagon of side 2 m is 12 m" is **True (T)**.

### Step 2: Calculate the area of a square floor with a side of 9 m.
- The formula for the area (A) of a square is:
\[ A = \text{side}^2 \]
- Substituting the given side length:
\[ A = 9 \, \text{m} \times 9 \, \text{m} = 81 \, \text{m}^2 \]
- The statement claims that the area of the carpet needed to cover the floor is 36 m², which is incorrect.
- Therefore, the statement "If the side of a square floor is 9 m, then the area of the carpet needed to cover the floor of the room is 36 m²" is **False (F)**.

### Step 3: Check if a square and a rectangle can have the same perimeter.
- Let's consider a square with a side length of 6 cm.
- The perimeter (P) of the square is:
\[ P = 4 \times \text{side} = 4 \times 6 \, \text{cm} = 24 \, \text{cm} \]
- Now, consider a rectangle with a length (L) of 8 cm and a width (W) of 4 cm.
- The perimeter of the rectangle is:
\[ P = 2 \times (L + W) = 2 \times (8 \, \text{cm} + 4 \, \text{cm}) = 2 \times 12 \, \text{cm} = 24 \, \text{cm} \]
- Since both the square and rectangle have the same perimeter of 24 cm, the statement "A square and rectangle can have the same perimeter" is **True (T)**.

### Final Answer:
- (i) T
- (ii) F
- (iii) T

So the final answer is **TFT**.