SMO 2015 Junior Round 1 Question 18

In the diagram below, a rectangle $ABCD$ is inscribed in a circle and $E$ is a point on the circumference of the circle. Given that $|AE|^2+|BE|^2+|CE|^2+|DE|^2=450$ and $|AB|\times|BC|=108$, find the perimeter of the rectangle.