A pair of similar triangles has areas $50{\text{cm}}^2$ and $162{\text{cm}}^2$.
Find the ratio of their corresponding angle bisectors.

$\frac{50}{162}=\frac{25}{81}$, and an angle bisector is a corresponding length, so the bisector ratio = $\sqrt{\frac{25}{81}}=\frac{5}{9}$, i.e. 5 : 9. The option 25 : 81 is the area ratio left unrooted, and 9 : 5 puts the triangles the wrong way round.