A wire is in the shape of a circle of radius 21 cm. It is bent to form a square. The side of the square is : `(pi = (22)/(7))`

Options

A. 22 cm
B. 33 cm
C. 44 cm
D. 66 cm

Answer

To solve the problem, we need to find the side of a square formed by bending a wire that was originally in the shape of a circle with a radius of 21 cm.

### Step-by-Step Solution:

1. **Find the Circumference of the Circle:**
The circumference \( C \) of a circle is given by the formula:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle. Here, \( r = 21 \) cm and \( \pi = \frac{22}{7} \).

Substituting the values:
\[ C = 2 \times \frac{22}{7} \times 21 \]

2. **Calculate the Circumference:**
First, calculate \( 2 \times \frac{22}{7} \):
\[ 2 \times \frac{22}{7} = \frac{44}{7} \]
Now multiply by 21:
\[ C = \frac{44}{7} \times 21 = \frac{44 \times 21}{7} \]
Simplifying \( \frac{21}{7} = 3 \):
\[ C = 44 \times 3 = 132 \text{ cm} \]

3. **Equate the Circumference to the Perimeter of the Square:**
When the wire is bent to form a square, the length of the wire remains the same. The perimeter \( P \) of a square with side length \( A \) is given by:
\[ P = 4A \]
Therefore, we have:
\[ 4A = 132 \]

4. **Solve for the Side Length \( A \):**
To find \( A \), divide both sides by 4:
\[ A = \frac{132}{4} = 33 \text{ cm} \]

### Final Answer:
The side of the square is \( 33 \) cm.