In an equiangular hexagon, all interior angles measure 120∘. An example of such a hexagon with side lengths 2, 3, 1, 3, 2, and 2 is shown below, inscribed in equilateral triangle ABC. Consider all equiangular hexagons with positive integer side lengths that can be inscribed in △ABC, with all six vertices on the sides of the triangle. What is the total number of such hexagons? Hexagons that differ only by a rotation or a reflection are considered the same.
(A)4(B)5(C)6(D)7(E)8
AB=BC=CA=6
x,y,z are positive integers. 6−x−y≥1⟹x+y≤5 Similarly, x+z≤5, y+z≤5.
Since hexagons that differ only by a rotation or a reflection are considered the same,
