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?(1 point)
In an equilateral triangle, the perpendicular bisector of any side is also the altitude of the triangle.
In a 30-60-90 right triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.
Since each side of the equilateral triangle is 36 inches long, each angle of the triangle is 60 degrees.
Therefore, the length of the altitude/perpendicular bisector of any side can be found using the relationships in a 30-60-90 right triangle.
In a 30-60-90 right triangle, the hypotenuse (longest side) is twice the length of the shorter leg.
Thus, the perpendicular bisector of any side in the equilateral triangle (which is also the altitude) will have a length of 36 ÷ 2 = 18 inches.