[Pythagorean Theorem (direct and inverse).]

One of the legs of a right triangle is 10 more than the other and 10 less than the hypotenuse. Find the hypotenuse of this triangle.
Let the first leg be $x$. Then the second leg is $x-10$, and the hypotenuse is $x+10$. By the Pythagorean theorem, $(x+10)^{2}=x^{2}+(x-10)^{2}$, from which $x=40$. Therefore, $x+10=50$.

## Answer

50.