A wire, when bent in the form of a square, encloses an area of 484 `cm^(2)`. Find :
(i) one side of the square
(ii) length of the wire
(iii) the largest area enclosed, if the same wire is bent to form a circle.

Answer

To solve the problem step by step, we will break it down into three parts as stated in the question.

### Step 1: Find one side of the square.
Given that the area of the square is 484 cm², we can use the formula for the area of a square:

\[ \text{Area} = \text{side}^2 \]

Let the side of the square be \( a \). Therefore, we have:

\[ a^2 = 484 \]

To find \( a \), we take the square root of both sides:

\[ a = \sqrt{484} = 22 \text{ cm} \]

### Step 2: Find the length of the wire.
The length of the wire is equal to the perimeter of the square. The formula for the perimeter \( P \) of a square is:

\[ P = 4 \times \text{side} \]

Substituting the value of the side we found:

\[ P = 4 \times 22 = 88 \text{ cm} \]

### Step 3: Find the largest area enclosed if the same wire is bent to form a circle.
When the wire is bent into a circle, the length of the wire becomes the circumference of the circle. The formula for the circumference \( C \) of a circle is:

\[ C = 2\pi r \]

Setting the circumference equal to the perimeter of the square:

\[ 2\pi r = 88 \]

To find the radius \( r \), we rearrange the equation:

\[ r = \frac{88}{2\pi} = \frac{44}{\pi} \]

Now, we can find the area \( A \) of the circle using the formula:

\[ A = \pi r^2 \]

Substituting the value of \( r \):

\[ A = \pi \left(\frac{44}{\pi}\right)^2 = \pi \cdot \frac{1936}{\pi^2} = \frac{1936}{\pi} \]

Using \( \pi \approx \frac{22}{7} \):

\[ A \approx \frac{1936 \times 7}{22} = 616 \text{ cm}^2 \]

### Summary of Answers:
1. One side of the square: **22 cm**
2. Length of the wire: **88 cm**
3. Largest area enclosed when bent into a circle: **616 cm²**