Correct solutions were submitted by
Farid Lian, Ron Welch, Bill Webb, David Stigant, Cee Ann Franklin,
Nancy Schwarzkopf, Matt Occhipinti, Juan Carlos Marivela, Burkart Venzke,
Lou Cairoli, Claudio Baiocchi and Bryan Fluhrer.
Suppose the rectangle's corners are labeled such that A is between B and C.
Draw perpendiculars from E to AB, AC, BD and CD,
labeling the intersections F, G, H and I, respectively.
Set w:=AF=CI, x:=BF=DI, y:=AG=BH and z:=CG=DH.
By the Pythagorean Theorem,
BE2=x2+y2
=(w2+y2)+(x2+z2)-(w2+z2)
=AE2+DE2-CE2
=1+9-4,
so BE is the square root of 6.
If the corners are labeled differently, BE becomes the square root of 12
(or imaginary).
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