I can solve it analytically, but I need some school-like elementary-geometry solution for this.
Let w = width and h = height of the rectangle ABCD. For any point E inside rectangle, except its boundary, let $f(E)=|AE| \cdot |EC| + |BE| \cdot |ED|$, question is: how to find point E inside this rectangle, except the points on the sides of this rectangle such that f(E) will be minimum. And find this minimum.