The ratio of the area of a regular polygon of `n` sides inscribed in a circle to that of the polygon of same number of sides circumscribing the same is 3:4. Then the value of `n` is

Explanation

To solve the problem, we need to find the value of \( n \) such that the ratio of the area of a regular polygon with \( n \) sides inscribed in a circle to the area of a regular polygon with \( n \) sides circumscribing the same circle is \( \frac{3}{4} \).

### Step-by-step Solution:

1. **Define the Areas of the Polygons**:
- Let \( S_1 \) be the area of the inscribed polygon.
- Let \( S_2 \) be the area of the circumscribed polygon.
- The area of a regular polygon with \( n \) sides inscribed in a circle of radius \( r \) is given by:
...