Traditional Culture Encyclopedia - Hotel accommodation - Suzhou ac hotel lounge

Suzhou ac hotel lounge

∵ The rectangle is folded along a straight line AC, and the point B falls on the point E,

∴∠BAC=∠EAC,AE=AB=CD,

Opposite sides of rectangular ABCD AB CD,

∴∠DCA=∠BAC,

∴∠EAC=∠DCA,

Let AE and CD intersect at f, then AF=CF,

∴AE-AF=CD-CF,

That is DF=EF,

∴DFFC=EFAF,

And ≈AFC =≈EFD,

∴△ACF∽△EDF,

∴DFFC=DEAC=35,

Let DF=3x and FC=5x, then AF=5x,

In Rt△ADF, AD=AF2? DF2=(5x)2? (3x)2=4x,

∫AB = CD = DF+FC = 3x+5x = 8x,

∴ADAB=4x8x= 12.

So the answer is: 12.