Since this is an equilateral triangle, we know that all sides are equal.

They give us the height of the equilateral triangle, which splits the equilateral triangle into 2 30-60-90 triangles.

Using the principles of a 30-60-90 triangle, we know that the sides will be in the ratio of x:x(sqrt)3:2x.

Plugging the side QS = 4(sqrt)3 into the ratio we get:
4: 4(sqrt)3 : 8

Now we know the hypotenuse of this isosceles triangle is equal to the side of the equilateral triangle (8). And, as an equilateral triangle, we know that all the sides are the same length. The perimeter is just adding up all 3 sides to get: 3(8) = 24. Answer is C.