Hinged squares
Drag the "hinges" to see how the squares move. Play with it a bit!
Where is the purple square the biggest?
At this point, convince yourself that the area of purple is bigger than red and blue added together.
Where is the purple square the smallest?
At this point, it's obviously smaller than the other two added together.
... so are you convinced that there must be a position where the purple is THE SAME as the other two added together?