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? the answer is either 36,18,9 or 18sqrt3
The perpendicular bisector of any side of an equilateral triangle is also the altitude of the triangle, which is also a line of symmetry.
In an equilateral triangle, the altitude is also the height of a 30-60-90 triangle formed by the altitude and one of the sides of the equilateral triangle. In a 30-60-90 triangle, the ratio of the lengths of the sides is 1:√3:2.
Since the side of the equilateral triangle is 36 inches long, the altitude (perpendicular bisector) is the shorter leg of the 30-60-90 triangle, which is 36/2 = 18 inches long.
Therefore, the length of the perpendicular bisector of any side of the stained glass window is 18 inches.
So, the correct answer is 18.