If the ratio of the angle bisectors of two similar

triangles is 2 : 5, then the ratio of theircorresponding areas is?

As we know that if two triangles are similar,then the ratio of any two corresponding segments(such as altitudes,medians or angle bisectors) equals the ratio of any two corresponding sides.

It means that ratio of the corresponding sides of two similar triangles = ratio of two corresponding angle bisectors.
Hence ratio of two corresponding sides = 2:5 

We also know that if two similar triangles have sides in the ratio x:y,then their areas are in the ratio $x^2:y^2$
Here in the question x:y = 2:5   then ​ $x^2:y^2=$4:25

$\therefore$Ratio of their corresponding areas is 4:25