In a regular triangular pyramid SABC, the medians of the base intersect at point O.

In a regular triangular pyramid SABC, the medians of the base intersect at point O. The area of triangle ABC is 16, the volume of the pyramid is 80. Find the length of the line segment OS.

V = (h * a ^ 2) / (4 * (3) ^ (1/2)) formula for the volume of a regular pyramid;
S = (((3) ^ (1/2)) / 4) * (a ^ 2) formula for the area of a regular triangle;
3 point 2: a ^ 2 = (S * 4) / ((3) ^ (1/2));
Since S is known to us, a ^ 2 = (16 * 4) / ((3) ^ (1/2));
3 point 1: h = (V * 4 * ((3) ^ (1/2))) / (a ^ 2);
Since we know V, h = (80 * 4 * ((3) ^ (1/2))) / (a ^ 2)
3 points 6 and 4 (in h we substitute a ^ 2): h = (80 * 4 * ((3) ^ (1/2))) / ((16 * 4) / ((3) ^ (1/2 ))) = (80 * 4 * (3 ^ (1/2)) * (3 ^ (1/2))) / (16 * 4) = 15