Question

special right triangles quick check
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)
9 inches
36 inches
$18\sqrt{3}$ inches
18 inches

Explanation:

Step1: Split triangle into 30-60-90 triangles

When you draw the perpendicular bisector of an equilateral triangle, it splits the triangle into two congruent 30-60-90 right triangles. The hypotenuse of each right triangle is the side of the equilateral triangle, so hypotenuse $= 36$ inches. The shorter leg is half the side of the equilateral triangle: $\frac{36}{2}=18$ inches.

Step2: Apply 30-60-90 side ratio

In a 30-60-90 triangle, the ratio of sides is shorter leg : longer leg : hypotenuse $=1:\sqrt{3}:2$. Let the longer leg (perpendicular bisector) be $x$. We know the shorter leg is 18 inches, so $x = 18\times\sqrt{3}$ inches.

Answer:

18√3 inches (Option: 18√3 inches)