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?
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:
Can you justify your answer?
Can you use the diagrams below to justify your results in two different ways?
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