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(A'B'C'D)/(ABCD)=9/16, ABCD rectangle

Source: (2021-) 2022 XV 15th Dürer Math Competition Finals Day 2 E11

December 12, 2022
geometryareasrectangle

Problem Statement

In rectangle ABCDABCD, diagonal ACAC is met by the angle bisector from BB at B′B' and the angle bisector from DD at D′D'. Diagonal BDBD is met by the angle bisector from AA at A′A' and the angle bisector from CC at C′C'. The area of quadrilateral A′B′C′D′A'B'C'D' is 916\frac{9}{16} the area of rectangle ABCDABCD. What is the ratio of the longer side and shorter side of rectangle ABCDABCD?
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