The numbers $20$, $99$, and $101$ form a Pythagorean triple. A right triangle has heights $x$, $\dfrac{20}{101}$, and $\dfrac{99}{101},$ where $x$ is the shortest height. What is $x?$
I know that the first sentence about the Pythagorean triple won't help. To solve for x, I take the longest side, square it, and subtract the square of the middle side. I get $\sqrt{\frac{99}{101}^2-\frac{20}{101}^2}$, which simplifies to $\sqrt{\frac{9401}{10201}}$. But my answer is wrong. What is the correct way to do this?
