# Task 2. (10 points)

In a right triangle $A B C$ (angle $C$ is right), medians $A M$ and $B N$ are drawn, the lengths of which are 19 and 22, respectively. Find the length of the hypotenuse of this triangle.
# Solution.

![](https://cdn.mathpix.com/cropped/2024_05_06_db367a0c3d9ccac4a1ceg-2.jpg?height=464&width=1124&top_left_y=590&top_left_x=518)

Let $AC = 2x$ and $BC = 2y$. By the Pythagorean theorem, we have

$$
\left\{\begin{array}{c}
(2 x)^{2}+y^{2}=19^{2} \\
x^{2}+(2 y)^{2}=22^{2}
\end{array} \Rightarrow 5 x^{2}+5 y^{2}=19^{2}+22^{2}=845 \Rightarrow\right.
$$

Answer: 26.