What is the height of an Equilateral Triangle on the GRE ?

The altitude of an equilateral triangle is    times the length of the base. If the length of the base (or any side of the equilateral triangle) is , we can express the altitude as:

If you forget that formula, you can easily derive it using Pythagorean Theorem. As you see in the above figure is a right triangle with hypotenuse equal to the length of the side or . Similarly the length of segment = .  Now we know the two sides of a right triangle and it’s enough to determine the third.