If the area of a square is numerically equal to its perimeter, then the length of each side is

Options

A. 1 units
B. 2 units
C. 3 units
D. 4 units

Answer

To solve the problem, we need to find the length of each side of a square when the area is numerically equal to its perimeter. Let's break it down step by step.

### Step-by-Step Solution:

1. **Define the Side Length**:
Let the length of each side of the square be \( a \).

2. **Calculate the Area**:
The area \( A \) of a square is given by the formula:
\[ A = a^2 \]

3. **Calculate the Perimeter**:
The perimeter \( P \) of a square is given by the formula:
\[ P = 4a \]

4. **Set Up the Equation**:
According to the problem, the area is numerically equal to the perimeter:
\[ a^2 = 4a \]

5. **Rearrange the Equation**:
To solve for \( a \), we rearrange the equation:
\[ a^2 - 4a = 0 \]

6. **Factor the Equation**:
We can factor out \( a \):
\[ a(a - 4) = 0 \]

7. **Solve for \( a \)**:
This gives us two possible solutions:
\[ a = 0 \quad \text{or} \quad a - 4 = 0 \]
Solving \( a - 4 = 0 \) gives:
\[ a = 4 \]

8. **Conclusion**:
Since the length of a side cannot be zero, we reject \( a = 0 \). Therefore, the length of each side of the square is:
\[ a = 4 \text{ units} \]

### Final Answer:
The length of each side of the square is 4 units.

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