Question

A regular hexagon is composed of 12 congruent 30 o -60 o -90 o triangles. If the length of the hypotenuse of one of those triangles is 18√3, find the perimeter of the hexagon.

Answer 1

[<BOC=30,<BCO=60,hence OC=2 BC,AC=2BC,so OC=AC,\[AC=18\sqrt{3}\]
or
<BOC=30,<AOB=30,<AOC=30+30=60,<OAC=60,
It is an equilateral triangle,sides are equal.\[AC=OC=18\sqrt{3}\]]