We have $f(3m) = (3m)^2 + 12 = 9m^2 + 12$, so $f(3m) = 3f(m)$ gives us $9m^2 + 12 = 3(m^2 + 12)$.  Expanding the right side gives $9m^2 +12 = 3m^2 + 36$. Simplifying gives $6m^2 = 24$, so $m^2 = 4$.  Since we are given that $m>0$, we have $m = \boxed{2}$.
Suppose $f (x ) = x^2 + 12$. If $m > 0$ and $f (3m) = 3(f (m))$, what is the value of $m$?
{'answer': '2', 'subject': 'Algebra', 'level': 4, 'unique_id': 'test/algebra/2637.json'}