Rectangles of same area
- James J Madden
How do I cut up the green rectangle to cover the red one? Many students want to cut parallel to the edges. But this does not always work. (What if the edges of the green rectangle are incommensurable with the edges of the red one?)
The solution is to rotate the green rectangle around the shared vertex, until a green side opposite the shared point passes through a red vertex adjacent to the shared one. Then cut off the green triangle that dips below the base of of the red rectangle, and use it to build a green parallelogram. Finally, use Euclid Proposition I:35.