If the area of a square is 48sq. Units, then what is the diagonal of the square ?

Options

A. `4sqrt(6)` units
B. `4sqrt(3)` units
C. `4sqrt(2)` units
D. `3sqrt(6)` units

Answer

To find the diagonal of a square when the area is given, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for the area of a square**:
The area \( A \) of a square is given by the formula:
\[ A = s^2 \]
where \( s \) is the length of one side of the square.

2. **Relate the area to the side length**:
Given that the area of the square is 48 square units, we can set up the equation:
\[ s^2 = 48 \]

3. **Solve for the side length \( s \)**:
To find \( s \), we take the square root of both sides:
\[ s = \sqrt{48} \]
We can simplify \( \sqrt{48} \):
\[ s = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3} \]

4. **Use the diagonal formula**:
The diagonal \( d \) of a square can be calculated using the formula:
\[ d = s\sqrt{2} \]
Substituting the value of \( s \):
\[ d = (4\sqrt{3})\sqrt{2} \]

5. **Simplify the expression for the diagonal**:
\[ d = 4\sqrt{3 \times 2} = 4\sqrt{6} \]

6. **Final answer**:
Therefore, the diagonal of the square is:
\[ d = 4\sqrt{6} \text{ units} \]