Sides of a cuboid are 3 cm, 4 cm, 12 cm then the length of the diagonal of a cuboid is

Options

A. 15
B. 7
C. 16
D. 13

Answer

To find the length of the diagonal of a cuboid with sides measuring 3 cm, 4 cm, and 12 cm, we can use the formula for the diagonal \( D \) of a cuboid, which is given by:

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

where \( l \) is the length, \( b \) is the breadth (or width), and \( h \) is the height of the cuboid.

### Step-by-Step Solution:

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

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

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

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

5. **Calculate the square root**:
\[ D = 13 \text{ cm} \]

### Final Answer:
The length of the diagonal of the cuboid is \( 13 \) cm.

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