∠∠EDC =∠DAE。

∴∠DAE∶∠EDA= 1∶3

∠∠DAE+∠EDA = 90

∴∠DAE=22.5 ∠EDA=67.5

In right-angle ABCD, AO=BO,

∴∠DAE∶∠ADO=22.5

∴∠ODE=67.5 -22.5 =45

∴△ODE is an isosceles right triangle.

In the rectangular ABCD, BD=AC= 10.

DO= half BD=5。

Let DE be x, then OE = X.

x？ +X？ =5? X=√2×5÷2

Answer: The length of DE is √2×5÷2.