Notes
five rectangles tiling a square solution

Solution to the Five Rectangles Tiling a Square Puzzle

Solution by Area of a Rectangle

In the diagram, $x$ is the height of the green rectangle. As the blue and green rectangles have the same width they also have the same height ($x$), so the height of the outer square is $2 + 2 x$.

The purple, green, and blue rectangles together have the same width as the orange rectangle and have triple its area, so their combined height is three times that of the orange. This leads to $2 x = 3 \times 2$, so $x = 3$. The outer square therefore has side length $8$ and so its area is $64$.