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Combinatorics Difficulty 5.0 AIME, harder Prove it United Kingdom

$PQRS$ is a square which has been divided into four regions: two identical rectangles, one square of area $9\text{ cm}^2$ and a second square of area $25\text{ cm}^2$ . What is the area of square $PQRS$ , in $\text{cm}^2$ ?

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