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Three congruent squares overlap as shown.

The areas of the three overlapping sections are $2\;\mathrm{cm}^2$, $5\;\mathrm{cm}^2$ and $8\;\mathrm{cm}^2$ respectively.

The total area of the non-overlapping parts of the squares is $117\;\mathrm{cm}^2$.

What is the side length of each square?






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This problem is taken from the UKMT Mathematical Challenges.
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