# Task 2. (2 points)

Does there exist a right triangle whose area is numerically equal to three times its hypotenuse?
Answer: Yes

Solution:

There are quite a few such triangles. Let's prove that there exists an isosceles one. We will set up an equation, denoting its side as $a$:

$$
\frac{a^{2}}{2}=3 \sqrt{2} a
$$

Obviously, this equation has a solution $a=6 \sqrt{2}$.