如图,在正方形ABCD和正方形CEFG中,AD＝6,CE＝2根号2,点F在CD上,连接DE,连接BG并延长交CD于点M,

参考：连接EG、DG,EG交DC于O；在正方形ABCD和正方形CEFG中BC＝CD＝DA＝6,EF＝EC＝CG＝2√2,∠BCD＝∠CEF＝∠ECG＝90°,CF＝√﹙EC²＋EF²﹚＝√﹙2√2﹚²＋﹙2√2﹚²]＝4；∵正方形CEFG的对角线相交于O∴OE＝½EG＝½CF＝OF＝OC＝2,OD＝DC－OC＝4,∠DCE＝∠DCG＝½∠ECG＝45°＝∠DCB－∠DCG＝∠BCG,EG⊥DC,∴⊿CBG≌⊿CDG≌⊿CDE﹙SAS﹚∴BG＝DG＝DE＝√﹙DO²＋OE²﹚＝√﹙4²＋2²﹚＝2√5,∠BHD＝180°－﹙∠CDE＋∠DMH﹚＝180°－﹙∠CBM＋∠CMB﹚＝∠BCD＝90°,DG²－DH²＝GH²＝EG²－EH²∴HD²－HE²＝GD²－GE²＝﹙2√5﹚²－4²＝4而HD＋HE＝DE＝2√5∴HD＝6√5/5,GH＝√﹙GD²－HD²﹚＝√[﹙2√5﹚²－﹙6√5/5﹚²]＝8√5/5,BH＝BG＋GH＝2√5＋8√5/5＝18√5/5.