smc

Let $a$ be the length of the shorter leg and $b$ be the longer leg. By the Pythagorean theorem, we can derive that $a^2+b^2=2$. Using area we can also derive that $2ab=1$. $(a+b{)}^2=3$ as given in the diagram, we can find that $(a-b{)}^2=1$ because $4ab=2$. This means that $b+a=\sqrt{3}$ and $b-a=1$. Adding the equations gives $b=\frac{\sqrt{3}+1}{2}$ and when $b$ is plugged in $a=\frac{\sqrt{3}-1}{2}$. Rationalizing the denominators gives us $\boxed{2-\sqrt{3}}$.