In a right-angled triangle, the medians drawn from the vertices of the acute angles are equal to $\sqrt{52}$ and $\sqrt{73}$. Find the hypotenuse of the triangle.
Let the legs be denoted by $x$ and $y$. Then, by the Pythagorean theorem, $x^{2} + y^{2} / 4 = 52$, and $y^{2} + x^{2} / 4 = 73$.

Adding these equations, we get $5 / 4\left(x^{2} + y^{2}\right) = 125 \Rightarrow x^{2} + y^{2} = 100$.

![](https://cdn.mathpix.com/cropped/2024_05_06_67482594d9a3488694ecg-26.jpg?height=318&width=640&top_left_y=670&top_left_x=709)

## Answer

10.