In a box whose dimensions are `12cm xx 4cm xx 3cm`, how long stick can be placed ?

Options

A. `13` cm
B. `14` cm
C. `15` cm
D. `16` cm

Explanation

To find the length of the longest stick that can be placed diagonally in a box with dimensions 12 cm, 4 cm, and 3 cm, we can use the formula for the diagonal of a rectangular box. The formula is derived from the Pythagorean theorem and is given by:

\[ d = \sqrt{l^2 + b^2 + h^2} \]

where:
- \( l \) is the length of the box,
- \( b \) is the breadth of the box,
- \( h \) is the height of the box.

### Step-by-Step Solution:

1. **Identify the dimensions of the box:**
- Length \( l = 12 \) cm
- Breadth \( b = 4 \) cm
- Height \( h = 3 \) cm

2. **Substitute the dimensions into the formula:**
\[ d = \sqrt{l^2 + b^2 + h^2} = \sqrt{12^2 + 4^2 + 3^2} \]

3. **Calculate the squares of the dimensions:**
- \( 12^2 = 144 \)
- \( 4^2 = 16 \)
- \( 3^2 = 9 \)

4. **Add the squares together:**
\[ 144 + 16 + 9 = 169 \]

5. **Take the square root of the sum:**
\[ d = \sqrt{169} = 13 \text{ cm} \]

### Final Answer:
The length of the longest stick that can be placed in the box is **13 cm**.

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