The maximum length of a pencil that can be kept in a rectangula box of dimensions `12 cm xx9 cm xx8 cm` is

Options

A. 13 cm
B. 17 cm
C. 18 cm
D. 19 cm

Answer

To find the maximum length of a pencil that can be kept in a rectangular box with dimensions 12 cm, 9 cm, and 8 cm, we need to calculate the diagonal of the box. The diagonal represents the longest straight line that can fit inside the box.

### Step-by-Step Solution:

1. **Identify the dimensions of the rectangular box**:
- Length (l) = 12 cm
- Breadth (b) = 9 cm
- Height (h) = 8 cm

2. **Use the formula for the diagonal (d) of a rectangular box**:
The formula to calculate the diagonal of a rectangular box is:
\[ d = \sqrt{l^2 + b^2 + h^2} \]

3. **Substitute the values into the formula**:
\[ d = \sqrt{(12)^2 + (9)^2 + (8)^2} \]

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

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

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

7. **Conclusion**:
The maximum length of the pencil that can be kept in the rectangular box is **17 cm**.