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Define the angle between the squares and the rectangle as $\theta$, where $\tan\theta\approx 2$ (looking at the image) Say the sidelength of the square is $s$ We have $s(3\sin\theta+2\cos\theta)=8$ and $s(3\sin\theta+\cos\theta)=7$ so $s\cos\theta=1$ and $3s\sin\theta=6$. So $s^2\cos^2\theta+s^2\sin^2\theta=5$, so $s=\sqrt{5}$