If the area of a square is numerically equal to the perimeter of the square, then the side of square is___

Options

A. 2 units
B. 3 units
C. 4 units
D. 5 units

Answer

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

### Step 1: Define the variables
Let the side length of the square be denoted as \( A \).

### Step 2: Write the formula for the area of the square
The area \( \text{Area} \) of a square is given by the formula:
\[ \text{Area} = A \times A = A^2 \]

### Step 3: Write the formula for the perimeter of the square
The perimeter \( \text{Perimeter} \) of a square is given by the formula:
\[ \text{Perimeter} = 4 \times A \]

### Step 4: Set up the equation
According to the problem, the area is numerically equal to the perimeter:
\[ A^2 = 4A \]

### Step 5: Rearrange the equation
To solve for \( A \), we can rearrange the equation:
\[ A^2 - 4A = 0 \]

### Step 6: Factor the equation
We can factor the left-hand side:
\[ A(A - 4) = 0 \]

### Step 7: Solve for \( A \)
Setting each factor to zero gives us:
1. \( A = 0 \)
2. \( A - 4 = 0 \) → \( A = 4 \)

### Step 8: Determine the valid solution
Since a side length cannot be zero (as a square cannot exist with a side length of zero), we discard \( A = 0 \). Thus, the valid solution is:
\[ A = 4 \]

### Conclusion
The side of the square is \( 4 \).

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