Question

The height of an equilateral triangle is four square root three what is the perimeter of the equilateral triangle

Answer 1

24

Explanation:

Recall that in an equilateral triangle, all the interior angles are the same, that is, all are 60°. If we look at the lower right 60° angle, we see that the side opposite this angle is the altitude (height) of the triangle.

In this problem the height is 4√3. What is the hypotenuse? We need to find the hypotenuse, because 3 times the length of this hypotenuse is the perimeter of the triangle.

Consider the sine function. Here, sin 60° = 4√3 / hyp, or:

√3 4√3

------- = -----------

2 hyp

thus, the length of the hypotenuse is 8 and the perimeter of the triangle is 3 times that, or 24.