Answer:
24
Step-by-step 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.
