2. Given that the altitude to the hypotenuse of right $\triangle A B C$ is 4. Then the minimum value of the area of $\triangle A B C$ is $\qquad$ .
2. 16 .

Let the lengths of the two legs of the right triangle $\triangle ABC$ be $a$ and $b$, and the length of the hypotenuse be $c$. From the area relationship, we have $ab = 4c$.
By the Pythagorean theorem, we know $c^2 = a^2 + b^2 \geq 2ab = 8c$.
Thus, $c \geq 8$. Therefore, $S_{\triangle ABC} = 2c \geq 16$.
When $a = b = 4\sqrt{2}$, the minimum value is achieved.