A circle and a square have same area. The ratio of the side of the square to the radius of the circle will be :

Options

A. (a) `sqrt(pi) :1`
B. (b) `1:sqrt(pi)`
C. (c) `pi^(2) : 1`
D. (d) `1 : pi`

Answer

To solve the problem, we need to find the ratio of the side of a square to the radius of a circle when both have the same area.

### Step-by-Step Solution:

1. **Define Variables**:
Let the side of the square be \( A \) and the radius of the circle be \( r \).

2. **Write the Area Formulas**:
- The area of the square is given by:
\[ \text{Area of square} = A^2 \]
- The area of the circle is given by:
\[ \text{Area of circle} = \pi r^2 \]

3. **Set the Areas Equal**:
Since the area of the square is equal to the area of the circle, we can write:
\[ A^2 = \pi r^2 \]

4. **Rearrange the Equation**:
To find the ratio \( \frac{A}{r} \), we can rearrange the equation:
\[ \frac{A^2}{r^2} = \pi \]

5. **Take the Square Root**:
Taking the square root of both sides gives:
\[ \frac{A}{r} = \sqrt{\pi} \]

6. **Express the Ratio**:
This means that the ratio of the side of the square to the radius of the circle is:
\[ \frac{A}{r} = \sqrt{\pi} : 1 \]

### Final Answer:
Thus, the ratio of the side of the square to the radius of the circle is \( \sqrt{\pi} : 1 \).