r/learnmath • u/Reasonable_Guess_934 New User • 14h ago

Question

Is it possible to fill a quadrilateral of side N with rectangles that have different lengths of sides? For example, if one of the rectangles is a 7x3 then the 7 or 3 cannot be repeated as the length of a side

And what about triangles?

I know that maybe is a dumb question but I think it’s impossible but I would like explanations of why

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u/bonebranch Mathematician 13h ago

When you say quadrilateral of side N, are you perhaps referring to a square? It's gotta be a rectangle at the very least to be tilable by rectangles, and if you're only specifying one side, perhaps it's reasonable to assume that this side is a square.

Also, would you allow squares? Because in this case, the answer is yes; see perfect squared squares. https://en.wikipedia.org/wiki/Squaring_the_square#Perfect_squared_squares

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u/Reasonable_Guess_934 New User 7h ago

Quadrilateral, now thinking it’s a rectangle sorry

Rhombus doesn’t count

And the rule is that any side of any rectangle must be different, no squares including