One of the following descriptions of a pair of similar triangles cannot possibly be true.
Which one is impossible?

For similar triangles the area ratio is forced to be the SQUARE of the side ratio. Sides 3 : 4 give areas ${\left(\frac{3}{4}\right)}^2=\frac{9}{16}$, never 3 : 4, so that description is impossible. Sides and areas can share a ratio only when the ratio is 1 : 1, as in the last option. The remaining two are consistent, since ${\left(\frac{\sqrt{2}}{\sqrt{3}}\right)}^2=\frac{2}{3}$.