Ah! Now this is a completely different kettle of fish.
The altitude of an equilateral triangle bisects and is perpendicular to the base and bisects the vertex to which it is constructed. Hence, the altitude, one-half of the base and the included side form a right triangle where the side of the equilateral triangle is the hypotenuse. Since we know that an interior angle of an equiangular triangle must measure 60 degrees, half of the bisected vertex must then measure 30 degrees, and the right angle is 90, we have a 30-60-90 right triangle. Using the long leg as unity, the sides of a 30-60-90 right triangle are in proportion:
Multiply by 8:
Hence, the hypotenuse of the 30-60-90, which is one side of the equilateral triangle, measures when the altitude is 8. Three such sides make the perimeter, so the perimeter must be
My calculator said it, I believe it, that settles it