A room is in the shape of cube and the length of the longest rod placed in it is 12 V3 m. The are a of the floor is:

Options

A. 36 sq. m
B. 144 sq. m
C. 64 sq. m
D. 96 sq. m

Answer

To solve the problem, we need to find the area of the floor of a cubic room given the length of the longest rod that can fit inside it.

### Step-by-Step Solution:

1. **Understand the Problem**:
The room is in the shape of a cube, and we are given the length of the longest rod that can fit inside it, which is 12√3 meters. The longest rod in a cube is the space diagonal.

2. **Formula for the Space Diagonal of a Cube**:
The formula for the length of the space diagonal (d) of a cube with side length (s) is:
\[ d = s\sqrt{3} \]

3. **Set Up the Equation**:
We know that the length of the longest rod (space diagonal) is equal to 12√3 meters. Therefore, we can set up the equation:
\[ s\sqrt{3} = 12\sqrt{3} \]

4. **Cancel Out √3**:
To simplify the equation, we can divide both sides by √3:
\[ s = 12 \]

5. **Calculate the Area of the Floor**:
The area of the floor of the cube is given by the formula for the area of a square (since the floor is a square):
\[ \text{Area} = s \times s = s^2 \]
Substituting the value of s:
\[ \text{Area} = 12 \times 12 = 144 \text{ square meters} \]

6. **Final Answer**:
The area of the floor is 144 square meters.