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

August 30, 2021 | education

| 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.

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