What should be side of square (in cm.) if its perimeter is equal to area?

Options

A. 6cm
B. 2cm
C. 4 cm
D. 8 cm

Answer

To solve the problem of finding the side of a square when its perimeter is equal to its area, we can follow these steps:

### Step 1: Understand the formulas
- The perimeter \( P \) of a square with side length \( x \) is given by:
\[ P = 4x \]
- The area \( A \) of a square with side length \( x \) is given by:
\[ A = x^2 \]

### Step 2: Set up the equation
Since the problem states that the perimeter is equal to the area, we can set the two formulas equal to each other:
\[ 4x = x^2 \]

### Step 3: Rearrange the equation
To solve for \( x \), we can rearrange the equation:
\[ x^2 - 4x = 0 \]

### Step 4: Factor the equation
Now, we can factor the left side of the equation:
\[ x(x - 4) = 0 \]

### Step 5: Solve for \( x \)
Setting each factor equal to zero gives us:
1. \( x = 0 \)
2. \( x - 4 = 0 \) → \( x = 4 \)

Since a side length cannot be zero, we take the positive solution:
\[ x = 4 \text{ cm} \]

### Conclusion
The side of the square should be \( 4 \) cm.

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