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What is the largest size that 35 square tiles can be, which fit in an area of $1080\times $1920?

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Tiles of equal size, apparently? – rschwieb Feb 12 '13 at 15:48
up vote 3 down vote accepted

If you accept rectangular tiles, you can fill the area by making tiles $\frac {1080}5 \times \frac {1920}7$ or $\frac {1080}7 \times \frac {1920}5$. These are $216 \times 274\frac 37$ and $154\frac 27 \times 384$. As you can see, in one direction the tile has a fractional dimension. You could also use $1080 \times \frac {1920}{35}$ or $\frac {1080}{35} \times 1920$ tiles, but I suspect that is not what you are looking for. For similar problems, you decide on the grid you want, starting by factoring the number of tiles, then divide the linear dimension by the corresponding factor.

In your title, you call for square tiles. You can't fill that area with $35$ square tiles. The best you can do is to use tiles with a side of $216$. Five of them will fill the $1080$ dimension, but the other direction will be $7 \times 216=1512$ and you will have $408$ left uncovered.

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I see nowhere in the question where the tiles are required to "fill". It just says "fit". I think the OP is trying to ask "What is the largest size that 35 square tiles can be, which still fit in this area?" – rschwieb Feb 12 '13 at 15:41
And by that I meant only to draw attention that readers can skip over the first part of the answer to the last part of the answer, which addresses that. – rschwieb Feb 12 '13 at 16:06

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