A room is 6m long, 5m broad and 4m high. The maximum length of rod that can be kept in the room is

Options

A. a. `sqrt61m`
B. b. `sqrt16m`
C. c. `sqrt36m`
D. d. `sqrt77m`

Answer

To find the maximum length of a rod that can be kept in a room with dimensions 6m (length), 5m (breadth), and 4m (height), we need to calculate the diagonal of the cuboid formed by the room. The formula for the diagonal \(d\) of a cuboid is given by:

\[ d = \sqrt{L^2 + B^2 + H^2} \]

where \(L\) is the length, \(B\) is the breadth, and \(H\) is the height of the cuboid.

### Step-by-Step Solution:

1. **Identify the dimensions of the room**:
- Length \(L = 6 \, m\)
- Breadth \(B = 5 \, m\)
- Height \(H = 4 \, m\)

2. **Substitute the dimensions into the diagonal formula**:
\[ d = \sqrt{L^2 + B^2 + H^2} \]
\[ d = \sqrt{6^2 + 5^2 + 4^2} \]

3. **Calculate the squares of the dimensions**:
- \(6^2 = 36\)
- \(5^2 = 25\)
- \(4^2 = 16\)

4. **Add the squares together**:
\[ d = \sqrt{36 + 25 + 16} \]
\[ d = \sqrt{77} \]

5. **Calculate the square root**:
- The approximate value of \(\sqrt{77}\) is about \(8.775\).

Thus, the maximum length of the rod that can be kept in the room is approximately \(8.775 \, m\).

### Final Answer:
The maximum length of the rod that can be kept in the room is approximately \(8.775 \, m\).

---