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Sliding Rectangles

Age 11 to 16
Challenge Level

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?