Notes
three congruent squares in a rectangle solution

Solution to the Three Congruent Squares in a Rectangle Puzzle

Solution by Similar Triangles

With the points labelled as in the diagram, triangles $E C D$ and $A B D$ are similar. The length scale factor can be seen to be $3$ (from $E C D$ to $A B D$) by considering $E C$ and $A B$. Therefore $D C$ is one third of $D B$ and so $\frac{2}{3}$rds of the rectangle is shaded.