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There’s a rectangle. A small rectangle is cut from the bigger rectangle ( not necessarily from the center). How will you partition the original rectangle after removing the cut such that the remaining areas of both the partitions are the same?

Here I was thinking to partition it by extending the diagonal line of the cut part. Is it correct and Is it the best approach ?

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    $\begingroup$ This is actually a great question. To whoever is reading, note that the smaller rectangle may not be similarly oriented as the bigger one. $\endgroup$
    – stoic-santiago
    Commented Jan 16, 2021 at 12:29

2 Answers 2

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Observe that any line through the center of a rectangle bisects its area.

Then the line joining the centers of two rectangles partitions the remaining areas equally.

enter image description here

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  • $\begingroup$ Thank you. Nicely explained. $\endgroup$
    – crazysra
    Commented Jan 16, 2021 at 14:45
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Which diagonal would you want to cut along? It wouldn't give an answer, let alone be the best approach.

Of course, "best" does not mean much in this context, but cutting along the line connecting the centres of the two rectangles would work and be the closest thing to a "best" approach I can think of.

To elaborate, it would among all the lines cutting the remaining area in half, it would be the only one to also cut both rectangles in half, provided they do not share their centres. Should that happen then any line passing through that point would work.

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  • $\begingroup$ Thank you . I understood where i went wrong. $\endgroup$
    – crazysra
    Commented Jan 16, 2021 at 14:45

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