The diagonal of a cuboid of length 5 cm, width 4 cm and height 3 cm is

Options

A. `5sqrt(2) cm`
B. `2sqrt(5) cm`
C. `12 cm`
D. 10 cm

Answer

To find the diagonal of a cuboid with given dimensions, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the dimensions of the cuboid**:
- Length (L) = 5 cm
- Width (B) = 4 cm
- Height (H) = 3 cm

2. **Use the formula for the diagonal (D) of a cuboid**:
\[ D = \sqrt{L^2 + B^2 + H^2} \]

3. **Calculate the squares of the dimensions**:
- \( L^2 = 5^2 = 25 \)
- \( B^2 = 4^2 = 16 \)
- \( H^2 = 3^2 = 9 \)

4. **Add the squares together**:
\[ L^2 + B^2 + H^2 = 25 + 16 + 9 = 50 \]

5. **Take the square root of the sum**:
\[ D = \sqrt{50} \]

6. **Simplify the square root**:
\[ D = \sqrt{25 \times 2} = 5\sqrt{2} \text{ cm} \]

### Final Answer:
The diagonal of the cuboid is \( 5\sqrt{2} \) cm.

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