Find the height of an equilateral triangle with side 4√ 3

Step one.

As we know, the height will divide the side in half in such a triangle, because it is also the median. Therefore, first we need to determine what half of the side of this triangle will be, knowing from the condition that the length of the side is 4√3:

4√3: 2 = 2√3.

Step two.

Now we can calculate what the length of the height in this triangle will be, using the well-known formula from the Pythagorean theorem:

√ ((4√3) ^ 2 – (2√3) ^ 2) = √ (48 – 12) = √36 = 6.

Answer: The height will be 6.