GRE Math : How to find the height of a right triangle

Example Questions

Example Question #1 : How To Find The Height Of A Right Triangle

An equilateral triangle has a side length of 4. What is its height?

Possible Answers:

2√2

4

2√3

2

16

Correct answer:

2√3

Explanation:

If an equilateral triangle is divided in 2, it forms two 30-60-90 triangles. Therefore, the side of the equilateral triangle is the same as the hypotenuse of a 30-60-90 triangle. The side lengths of a 30-60-90 triangle adhere to the ratio x: x√3 :2x. since we know the hypothesis is 4, we also know that the base is 2 and the height is  2√3.