Median of an equilateral = x cm
In an equilateral triangle median is an altitude.
Let the side of triangle be a cm
(AB)2 = (AD)2 + (BD)2
(a)2 = (x)2 + \((\frac{a}{2})^2\) c
a = \(\frac{2x}{\sqrt{3}}\) cm
Area of an equilateral triangle = \(\frac{\sqrt3a^2}{4}\) = \(\frac{\sqrt{3}\times{2x}\times{2x}}{{4}\times\sqrt{3}\times\sqrt{3}}\) = \(\frac{\sqrt3a^2}{3}\)
= \(\frac{\sqrt{3}\times\sqrt{3x}^2}{{3}\times\sqrt{3}}\) = \(\frac{x^2}{\sqrt{3}}\) cm2
