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
The perpendicular bisector of a side of an equilateral triangle passes through the midpoint of that side and is also an altitude of the triangle.
Since the sides of the equilateral triangle are all equal, the length of the perpendicular bisector is also equal to the length of the altitude.
In an equilateral triangle, the length of the altitude can be found using the formula:
altitude = (sqrt(3)/2) * side length
In this case, the side length is 36 inches, so the length of the perpendicular bisector is:
altitude = (sqrt(3)/2) * 36
altitude = (1.732/2) * 36
altitude = 0.866 * 36
altitude ≈ 31.176 inches
Since the given options are 36, 18, and 9 inches, the closest value is 36 inches.