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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?
NRICH is part of the family of activities in the Millennium Mathematics Project.