UKMT Cayley Olympiad, 2020

Geometry Difficulty 2.0 Junior Prove it United Kingdom

Two squares $ABCD$ and $BEFG$ share the vertex $B$ , with $E$ on the side $BC$ and $G$ on the side $AB$ , as shown. The length of $CG$ is $9$ cm and the area of the shaded region is $47$ cm $^2$ . Calculate the perimeter of the shaded region.

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