用一矩形钢板ABCD加工某四边形工件ADCE,已知AB=2dm,BC=1dm,CE⊥BD于E,则该工件AE边长为?

√65/5

AB=2,BC=1,
则,BD=√5
CE=1×2/√5=2/√5
DE=√(CD^2-CE^2)=4/√5
cos∠ADB=AD/BD=1/√5
∴AE=√(AD^2+DE^2-2AD*DE*coscos∠ADB)
=√[1+16/5-2×1×(4/√5)×(1/√5)]
=√(13/5)
=(1/5)√65