The perimeter of a regular triangle inscribed in a circle is 45 find the side of a regular octagon inscribed in the same circle.

1. Find the side of a regular inscribed triangle if its perimeter is 45:

P = 3 a3;

a3 = 45/3 = 15.

2. Formula for the radius of the circumscribed circle around a regular triangle R = a3 / √3. Find the radius:

R = 15 / √3 = 8.66.

3. Formula for the radius of the circumscribed circle around a regular octagon R = a8 * √ ((1 + √2) / √2). Find the side of the octagon:

a8 = R / √ ((1 + √2) / √2) = 8.66 / √ ((1 + √2) / √2) = 6.63.