MathNet 2024-part-06 — 165 problems (EN–VI) Question 136

Let $ABCD$ be a convex quadrilateral with area $202$, $AB=4$, and $\angle A=\angle B=90^{\circ}$ such that there is exactly one point $E$ on line $CD$ satisfying $\angle AEB=90^{\circ}$. Compute the perimeter of $ABCD$.