Use what you know about the relationships in 30-60-90 right triangles to solve the following problem. A stained-glass window is in the shape of an equilateral triangle with sides that are 36 inches long. How long is the perpendicular bisector of any side?
Options
9 inches
18 square root of 3 inches
18 inches
36 inches
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.