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Let's say I have a puzzle, which says it has 1000 pieces. I also know it's a 4:3 ratio picture that I'm trying to put together. How do I calculate the width & height in number of pieces?

I know that if I knew the puzzle was 1000 pieces wide, it would have a 750 pieces height, since thats a 4:3 ratio. But I don't know the width/height, only the calculated resolution.

? x ? = 1000

I started with a square root, giving me the number of ± 31.62, which would be right if the puzzle was a square, but it's in the 4:3 ratio.

Thanks in advance!

Bran van der Meer
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  • I think that it goes as follows: If $l$ is the number of pieces along the short side, then $\frac{4}{3}l$ is the number of pieces along the long side. The total number of pieces is then $\frac{4}{3}l^2=1000$, and we can solve for $l$. – Giuseppe Negro Feb 13 '14 at 22:29

2 Answers2

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Here is a description of why Bran van der Meer's answer works:

Consider $$ wh=1000 $$ and $$ \frac wh=\frac43 $$ Multiply these to get $$ w^2=1000\times\frac43 $$ Divide them to get $$ h^2=1000\times\frac34 $$

robjohn
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Hint: If the number of pieces in the short direction is $x$, the number in the long direction is $\frac 43x$. The total number of pieces is then ??? Now solve for $x$

Ross Millikan
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