A wire is looped in the form of a circle of radius 35 cm. If it is rebent in the form of a square,what will be the length of each side of the square?

Answer

To solve the problem step by step, we need to find the length of each side of the square formed by rebending a wire that was originally in the shape of a circle with a radius of 35 cm.

### Step-by-Step Solution:

1. **Calculate the circumference of the circle:**
The circumference (perimeter) of a circle is given by the formula:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle.

Here, the radius \( r = 35 \) cm. We will use \( \pi \approx \frac{22}{7} \) for our calculations.

Substituting the values:
\[ C = 2 \times \frac{22}{7} \times 35 \]

2. **Simplify the calculation:**
First, calculate \( 2 \times \frac{22}{7} \):
\[ 2 \times \frac{22}{7} = \frac{44}{7} \]
Now multiply this by 35:
\[ C = \frac{44}{7} \times 35 \]
We can simplify \( 35 \) as \( \frac{35 \times 7}{7} = 245 \):
\[ C = \frac{44 \times 35}{7} = \frac{1540}{7} = 220 \text{ cm} \]

3. **Set the perimeter of the square equal to the circumference of the circle:**
When the wire is reshaped into a square, the perimeter of the square is equal to the circumference of the circle:
\[ P_{\text{square}} = 4a \]
where \( a \) is the length of each side of the square.

Since the perimeter of the square is equal to the circumference of the circle:
\[ 4a = 220 \]

4. **Solve for the length of each side of the square:**
To find \( a \), divide both sides by 4:
\[ a = \frac{220}{4} = 55 \text{ cm} \]

### Final Answer:
The length of each side of the square is **55 cm**.