TIMO - 2021 - Grade 9 - Heat Round - Paper 1 Question 20

In the figure, $ABCD$ is a square with side $a$. Points $E,F$ lie on diagonal $AC$, and the areas of $ABED$, $BEDFC$, $DFC$ are in the ratio $1:3:2$. Find $EF$ in surd form in terms of $a$.