Sliding Rectangles

  



The picture to the right shows a rectangle with a diagonal drawn on it. An arbitrary point, $P$, has been placed on the diagonal. The two shaded rectangles, $A$ and $B$, have a common vertex at $P$. 




Which of these two rectangles has the greater area?

Can you find more than one way to justify your answer?

Below is an interactive version of the picture above. You may find it helpful to click and drag point $P$, and see how the two rectangles $A$ and $B$ change: