Answer
From the definition of a midpoint, we know that a 45-45-90 triangle is formed. Because of this, we know that the hypotenuse is $\sqrt2$ greater than the leg. Thus:
$ \frac{RT}{RS} = \frac{1}{\sqrt2} = \frac{\sqrt2}{2}$
RT is twice the value of RO, so we obtain:
$ \frac{RT}{R0} = \frac{2}{\sqrt2} = \frac{2\sqrt2}{2}=\sqrt2$
