The area of square is `(16)/(pi)` area of a circle. The ratio of the side of the square to the diameter of the circle is

Options

A. `3 : 1`
B. ` 2 : 1`
C. ` pi : 1`
D. ` sqrt(2) pi : 1`

Answer

To solve the problem, we need to find the ratio of the side of the square to the diameter of the circle given that the area of the square is \(\frac{16}{\pi}\) times the area of the circle.

### Step-by-Step Solution:

1. **Understanding the Areas**:
- Let the side of the square be \(a\).
- The area of the square is given by \(a^2\).
- Let the radius of the circle be \(r\).
- The area of the circle is given by \(\pi r^2\).

2. **Setting Up the Equation**:
- According to the problem, the area of the square is \(\frac{16}{\pi}\) times the area of the circle:
\[ a^2 = \frac{16}{\pi} \cdot \pi r^2 \]
- Simplifying this gives:
\[ a^2 = 16r^2 \]

3. **Finding the Relationship Between \(a\) and \(r\)**:
- Taking the square root of both sides, we find:
\[ a = 4r \]

4. **Finding the Diameter of the Circle**:
- The diameter \(d\) of the circle is given by:
\[ d = 2r \]

5. **Finding the Ratio of the Side of the Square to the Diameter of the Circle**:
- We need to find the ratio \(\frac{a}{d}\):
\[ \frac{a}{d} = \frac{4r}{2r} \]
- Simplifying this gives:
\[ \frac{a}{d} = \frac{4}{2} = 2 \]

### Final Answer:
The ratio of the side of the square to the diameter of the circle is \(2\).