Find the side of an equilateral triangle if the radius of the circumscribed circle around it is 10 cm.

The radius of a circle circumscribed about an equilateral (regular) triangle can be expressed through its side:
R = √3 / 3 * a,
where R is the radius of the circumscribed circle, and is the side of a regular triangle.
√3 / 3 * a = 10;
a = 3 * 10 / √3;
a = 30 / √3.
Let’s get rid of the irrationality in the denominator by multiplying the fraction by √3:
a = 30√3 / (√3) ^ 2 = 30√3 / 3 = 10√3 (cm).
Answer: a = 10√3 cm.