The numerical value of the perimeter of a square exceeds that of its area by 4 . What is the side of the square ?
(a)1 unit
(b)2 unit
(c)3 unit
(d)4 unit

Options

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

Answer

To solve the problem, we need to find the side length of a square given that the numerical value of its perimeter exceeds its area by 4.

### Step-by-Step Solution:

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

2. **Write the formulas for perimeter and area**:
- The perimeter \( P \) of a square is given by the formula:
\[ P = 4A \]
- The area \( A \) of a square is given by the formula:
\[ A = A^2 \]

3. **Set up the equation based on the problem statement**:
According to the problem, the perimeter exceeds the area by 4. Therefore, we can write the equation:
\[ P - A = 4 \]
Substituting the formulas for perimeter and area, we get:
\[ 4A - A^2 = 4 \]

4. **Rearrange the equation**:
Rearranging the equation gives us:
\[ A^2 - 4A + 4 = 0 \]

5. **Factor the quadratic equation**:
The quadratic equation \( A^2 - 4A + 4 = 0 \) can be factored as:
\[ (A - 2)(A - 2) = 0 \]
This simplifies to:
\[ (A - 2)^2 = 0 \]

6. **Solve for \( A \)**:
Setting the factor equal to zero gives:
\[ A - 2 = 0 \implies A = 2 \]

7. **Conclusion**:
The side length of the square is \( 2 \) units.

### Final Answer:
The side of the square is \( 2 \) units, which corresponds to option (b).

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