A square of the perimeter is q units, then its area is sq.units

Options

A. (q^2)/16
B. (q^2)
C. (q^2)/4
D. (q^2)/64

Answer

To solve the problem, we need to find the area of a square when its perimeter is given as \( q \) units.

### Step-by-Step Solution:

1. **Understanding the Perimeter of a Square**:
The perimeter \( P \) of a square is the sum of the lengths of all four sides. Since all sides of a square are equal, we can express the perimeter as:
\[ P = 4 \times \text{side} \]

2. **Setting Up the Equation**:
We are given that the perimeter \( P \) is equal to \( q \) units. Therefore, we can write:
\[ 4 \times \text{side} = q \]

3. **Finding the Length of One Side**:
To find the length of one side of the square, we rearrange the equation:
\[ \text{side} = \frac{q}{4} \]

4. **Calculating the Area of the Square**:
The area \( A \) of a square is given by the formula:
\[ A = \text{side}^2 \]
Substituting the expression we found for the side:
\[ A = \left(\frac{q}{4}\right)^2 \]

5. **Simplifying the Area**:
Now we simplify the expression:
\[ A = \frac{q^2}{16} \]

6. **Final Result**:
Thus, the area of the square in square units is:
\[ A = \frac{q^2}{16} \text{ square units} \]