Question

What is the height, x, of the equilateral triangle?

Answer 1

D:
`4\sqrt3`

Explanation:

Draw the height. You notice you have split the triangle in two right triangles of sides 8 (the hypotenuse), 4 (half the horizontal side) and x. Let's apply Pythagorean theorem to the triangle:
`8^2 = 4^2+x^2 \rightarrow 64=16+x^2 \rightarrow x^2= 48 = 4^2*3\\x= \sqrt48 = 4\sqrt3`