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HMMT Geometry 2019/2: Simple rectangle geometry with equal areas

Source:

February 17, 2019
HMMTgeometryrectangle

Problem Statement

In rectangle ABCDABCD, points EE and FF lie on sides ABAB and CDCD respectively such that both AFAF and CECE are perpendicular to diagonal BDBD. Given that BFBF and DEDE separate ABCDABCD into three polygons with equal area, and that EF=1EF = 1, find the length of BDBD.
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