# Trapezoid Riddle

Geometry Level 4

Trapezoid $$ABCD$$ has $$\angle C=\angle D=90^\circ$$ and $$AB=170$$ with $$AD || BC,$$ as shown above. Point $$E$$ is picked on $$DC$$ such that $$AE = 100$$ and $$BE = 90.$$ All of the segments $$AD, DE, EC,$$ and $$CB$$ have integer lengths.

What is the perimeter of trapezoid $$ABCD?$$

×