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?
In an equilateral triangle, the perpendicular bisector of any side is also the altitude of the triangle. In such a triangle, the altitude can be found using Pythagoras' theorem.
Let's denote the length of the perpendicular bisector as "x".
Then the length of the side of the triangle is 36 inches.
Using Pythagoras' theorem, we have:
x^2 = (36/2)^2 + 36^2
x^2 = 18^2 + 36^2
x^2 = 324 + 1296
x^2 = 1620
Taking the square root on both sides to solve for x, we get:
x = √(1620)
x ≈ 40.31
So, the length of the perpendicular bisector or altitude of the equilateral triangle is approximately 40.31 inches.