If the area of a square is 24 sq. units then what is the perimeter of the square ?

Options

A. `2sqrt(6)` units
B. `4sqrt(6)` units
C. `16sqrt(6)` units
D. `8sqrt(6)` units

Answer

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

### Step-by-Step Solution:

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

2. **Set up the equation using the given area**:
We know that the area of the square is 24 square units. Therefore, we can write:
\[ x^2 = 24 \]

3. **Solve for \( x \)**:
To find \( x \), we take the square root of both sides:
\[ x = \sqrt{24} \]
We can simplify \( \sqrt{24} \):
\[ \sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6} \]

4. **Calculate the perimeter**:
The perimeter \( P \) of a square is given by the formula:
\[ P = 4 \times x \]
Substituting \( x = 2\sqrt{6} \) into the perimeter formula:
\[ P = 4 \times (2\sqrt{6}) = 8\sqrt{6} \]

5. **State the final answer**:
Therefore, the perimeter of the square is:
\[ P = 8\sqrt{6} \text{ units} \]