Find the area of square whose perimeter is 96 m. 

Options

A. `384 m^(2)`
B. `576 m^(2)`
C. `2304 m^(2)`
D. `144 m^(2)`

Answer

To find the area of a square whose perimeter is 96 meters, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between perimeter and side length**:
The perimeter \( P \) of a square is given by the formula:
\[ P = 4 \times \text{side length} \]
Let's denote the side length of the square as \( x \).

2. **Set up the equation using the given perimeter**:
We know the perimeter is 96 meters, so we can write:
\[ 4x = 96 \]

3. **Solve for the side length \( x \)**:
To find \( x \), divide both sides of the equation by 4:
\[ x = \frac{96}{4} = 24 \text{ meters} \]

4. **Calculate the area of the square**:
The area \( A \) of a square is given by the formula:
\[ A = \text{side length} \times \text{side length} = x^2 \]
Substituting the value of \( x \):
\[ A = 24 \times 24 = 576 \text{ square meters} \]

5. **Conclusion**:
Therefore, the area of the square whose perimeter is 96 meters is:
\[ \text{Area} = 576 \text{ m}^2 \]