SEAMO 2027 - Paper F - SET 04 - Self-study Question 14

Question 14

$ABCD$ is a square with $AB=m$, and $AEFG$ is a rectangle such that $E$ lies on side $BC$ and $D$ lies on side $FG$. Given that $AE=n$, what is the length of side $EF$?

Original source image, preserving the printed mathematical labels and any disclosed source discrepancy.

Question illustration

$\frac{m^2}{n}$
$\frac{n^2}{m}$
$\frac{\sqrt2\,m^2}{n}$
$\frac{\sqrt2\,n^2}{m}$
None of the above