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In a 30-60-90 right triangle, the lengths of the sides are in a ratio of 1:√3:2.
Since the equilateral triangle has sides of 36 inches, each side of the triangle can be divided into two congruent segments by its perpendicular bisector.
Therefore, the length of the perpendicular bisector is 1/2 of the length of the corresponding side.
Therefore, the length of the perpendicular bisector of any side is (1/2) * 36 inches = 18 inches.
So the correct answer is 18 inches.