How to arrange 3 rectangles in a big rectangle
I have a big rectangle of 100x100. I want to arrange 3 rectangle whose original size is 40x40, 40x40 and 10x10 in a 100x100 rectangle.
Here we can increase any width or height or both by specific ratio of all 3 rectangles, so all 3 rectangle should cover complete rectangle of 100x100, complete space should be occupied.
Thanks
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$\begingroup$Reformulating a little more handy:
We have a $10\times 10$ square and want to cover it with rectangles of side lengths
$$a\times b, 4a\times 4b \text{ and } 4a\times 4b$$
Where $a,b$ can be chosen.
The area of the three rectangles will be $33ab$ so $100 = 33ab \Rightarrow b = \frac{100}{33a}$. I doubt it's even possible to enforce this (i.e. that they don't overlap)
If you allow overlapping, the problem is trivial with $a = b = \frac{10}4$ so the bigger rectangles are $10\times 10$ and you just place them atop the rectangle and the smaller rectangle is to be placed anywhere within the others.
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