The length of the longest pole that can be kept in a room `(12 m xx 9 m xx 8 m)` is

Options

A. 29 m
B. 21 m
C. 19 m
D. 17 m

Explanation

To find the length of the longest pole that can be kept in a room with dimensions \(12 \, \text{m} \times 9 \, \text{m} \times 8 \, \text{m}\), we need to calculate the diagonal of the rectangular room. The formula for the diagonal \(d\) of a rectangular cuboid is given by:

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

where:
- \(L\) is the length of the room,
- \(B\) is the breadth of the room,
- \(H\) is the height of the room.

### Step-by-Step Solution:

1. **Identify the dimensions of the room**:
- Length \(L = 12 \, \text{m}\)
- Breadth \(B = 9 \, \text{m}\)
- Height \(H = 8 \, \text{m}\)

2. **Substitute the dimensions into the diagonal formula**:
\[ d = \sqrt{12^2 + 9^2 + 8^2} \]

3. **Calculate the squares of each dimension**:
- \(12^2 = 144\)
- \(9^2 = 81\)
- \(8^2 = 64\)

4. **Add the squares together**:
\[ 144 + 81 + 64 = 289 \]

5. **Take the square root of the sum**:
\[ d = \sqrt{289} = 17 \, \text{m} \]

Thus, the length of the longest pole that can be kept in the room is **17 meters**.