The perimeter of a regular triangle inscribed in a circle is 45 cm, find the side of a regular hexagon.

It is known from the condition that the perimeter of a regular triangle inscribed in a circle is 45 cm. Find the length of the side of a regular hexagon.

Let’s start by remembering that the side of a regular hexagon is equal to the radius of the circumscribed circle.

That is, we need to calculate the radius of the circle.

Let’s recall the formula for finding the radius of a circle circumscribed around a regular triangle:

R = a√3 / 3, where a is the side of the triangle.

To calculate the side of a regular triangle, apply the formula P = 3a;

a = P / 3.

We calculate:

a = 45/3 = 15 cm;

We are looking for a radius:

R = 15√3 / 3 = 5√3 cm.

Answer: 5√3 cm side of the hexagon.