Using Heron’s formula, $s = 12$, area $= \sqrt12 \times 5 \times 4 \times 3 = 12\sqrt5$. The shortest altitude corresponds to the longest side (9): $h = \frac{2 \times 12\sqrt5}9 = \frac{24\sqrt5}9 = \frac{8\sqrt5}3$. \boxed{\dfrac{8\sqrt5}3} - Dyverse