A nucleus of mass number 189 splits into two nuclei having mass...

The relation between radius $\left(R\right)$ of nuclei and mass number $\left(A\right)$ is given by, $R = {R}_{0}A\dfrac{1}{3}$, where ${R}_{0}$ is fermi constant.

Thus, $\dfrac{{R}_{1}}{{R}_{2}} = \left(\dfrac{{A}_{1}}{{A}_{2}}\right)\dfrac{1}{3} = \left(\dfrac{125}{64}\right)\dfrac{1}{3} = \dfrac{5}{4}$.