### Instruction: 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.### Response: I remember that the median to the hypotenuse of any right triangle is half the length of the hypotenuse, so I can use that fact to find the length of the hypotenuse.
Let x be the length of a leg of the triangle, and let y be the length of the hypotenuse.
Then, by the Pythagorean theorem, I have x^2 + x^2 = y^2.
Also, by the given fact, I have 10 = y/2, or y = 20.
Substituting y = 20 into the Pythagorean equation, I get x^2 + x^2 = 20^2, or 2x^2 = 400.
Dividing both sides by 2, I get x^2 = 200, or x = sqrt(200).
I can simplify sqrt(200) by factoring out the largest perfect square that divides 200, which is 100.
So, x = sqrt(100)*sqrt(2), or x = 10*sqrt(2).