2025 VIMC keystage2-EMIC individual Question 11

In the diagram below, $ABC$ is a right triangle with $\angle A=90^\circ$, $AB=15$ cm and $AC=36$ cm. Let $D$ and $E$ be points on $BC$ such that $BD=DE=EC$. What is the value, in cm², of $AD^2+AE^2$?