The length of the median to the hypotenuse of an isosceles, right triangle is $10$ units.  What is the length of a leg of the triangle, in units? Express your answer in simplest radical form.
The length of the median to the hypotenuse is half the length of the hypotenuse, so the hypotenuse is $10\cdot2=20$ units long. Since the right triangle is isosceles, the length of a leg is $20/\sqrt{2}=\boxed{10\sqrt{2}}$ units.