What is the length of the longest needle that can be accommodated in a rectangular box , if its dimensions being 20 cm `xx` 5 cm `xx` 4 cm ?

Answer

To find the length of the longest needle that can be accommodated in a rectangular box with dimensions 20 cm, 5 cm, and 4 cm, we need to calculate the diagonal of the box. The diagonal can be found using the formula:

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

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

### Step-by-Step Solution:

1. **Identify the dimensions of the box:**
- Length \( l = 20 \) cm
- Breadth \( b = 5 \) cm
- Height \( h = 4 \) cm

**Hint:** Write down the dimensions clearly to avoid confusion.

2. **Substitute the dimensions into the diagonal formula:**
\[ d = \sqrt{l^2 + b^2 + h^2} = \sqrt{20^2 + 5^2 + 4^2} \]

**Hint:** Make sure to square each dimension correctly.

3. **Calculate the squares of each dimension:**
- \( 20^2 = 400 \)
- \( 5^2 = 25 \)
- \( 4^2 = 16 \)

**Hint:** Double-check your calculations for accuracy.

4. **Add the squared values together:**
\[ 400 + 25 + 16 = 441 \]

**Hint:** Keep track of your addition step-by-step to avoid mistakes.

5. **Take the square root of the sum:**
\[ d = \sqrt{441} \]

**Hint:** Remember that the square root of a number gives you the length of the diagonal.

6. **Calculate the square root:**
\[ d = 21 \text{ cm} \]

**Hint:** Verify that \( 21^2 = 441 \) to confirm your answer.

### Final Answer:
The length of the longest needle that can be accommodated in the rectangular box is **21 cm**.