The median of a right triangle, drawn to the hypotenuse, divides it into two triangles with perimeters of 8 and 9. Find the sides of the triangle.

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Let's denote the legs of the triangle as $a$ and $b(a<b)$. Since the median of a right triangle drawn from the vertex of the right angle is equal to half the hypotenuse, then $b-a=9-$ $8=1$, and the hypotenuse is equal to $8-a$. By the Pythagorean theorem, $a^{2}+b^{2}=(8-a)^{2}$. From the system, we find that $a=3, b=$ 4.

## Answer

$3,4,5$.