well the line passing from one point through the triangle to the base of another side can be calculated using pythagoras theorem

12^2 - 6^2 = (x+y)^2

x+y = sqrt(108)

the gravity point (where all the internal lines meet) is always 2/3 from the apex or 1/3 from the base

therefore

y = (2/3)sqrt(108)

x = (1/3)sqrt(108)