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2022 MMATHS Individual p5 - folding a rectange

Source:

October 1, 2023
geometryrectangleMMATHS

Problem Statement

Holding a rectangular sheet of paper ABCDABCD, Prair folds triangle ABDABD over diagonal BDBD, so that the new location of point AA is A′A'. She notices that A′C=13BDA'C =\frac13 BD. If the area of ABCDABCD is 27227\sqrt2, find BDBD.
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