# The median of an equilateral triangle is 12 root of three. find his side.

The median of an equilateral triangle is 12 root of three. find his side.
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William Collins
The median in an equilateral triangle is both the altitude and the bisector.
for example given a triangle. ABC, where BH is the median.
maybe she and height$⇒$ triang. ABN - rectangular.
all angles in an equilateral triangle $={60}^{\circ }$ each
times $\mathrm{\angle }A=60⇒\mathrm{\angle }ABH={30}^{\circ }$. In straight. triangle leg lying opposite $\mathrm{\angle }$ at ${30}^{\circ }=$ half of the hypotenuse$⇒AH=1/2AB⇒AB=2AH$
Now, according to the Pythagorean theorem, we compose: $\left(2AH{\right)}^{2}=\left(12\sqrt{3}{\right)}^{2}+A{H}^{2}$
$4A{H}^{2}=432+A{H}^{2}$
$3A{H}^{2}=432$
$A{H}^{2}=144$
АН=12
AC=2AH=24cm