MathDB

S <= (a^2+b^2+c^2)/ 4\sqrt3 1993 Kyiv City MO 11.4

Source:

July 21, 2021

geometrygeometric inequality

Problem Statement

Let

a, b, c

be the lengths of the sides of a triangle, and let

S

be it's area. Prove that

S \le \frac{a^2+b^2+c^2}{4\sqrt3}

and the equality is achieved only for an equilateral triangle.