IMAS 2021–2022 Junior Division, Round 2 Question 2

Question 2

In the diagram below, $ABCD$ is a rectangle, where $AB=8$ cm and $BC=4$ cm. Let the angle bisector from $D$ intersect $AB$ at $E$. Find the distance, in cm, from $E$ to $AC$.

Question illustration

$\frac{3\sqrt2}{2}$
$\frac{4\sqrt2}{5}$
$\frac{4\sqrt5}{5}$
$\frac{2\sqrt5}{5}$
$\frac{4\sqrt2}{5}$