如图，BD是∠ABC的角平分线，DE⊥AB于点E，DF⊥BC于点F，S△ABC=36cm2，AB=18cm，BC=12cm，则DE的长为125125cm．

Question

如图，BD是∠ABC的角平分线，DE⊥AB于点E，DF⊥BC于点F，S_△ABC=36cm²，AB=18cm，BC=12cm，则DE的长为

(12)/(5)

(12)/(5)

cm．

Answer 1

∵BD是∠ABC的角平分线，DE⊥AB，DF⊥BC，∴DE=DF，∵S△ABC=36cm2，S△BCD=12BC•DF，又∵S△ABC=S△ABD+S△BCD，AB=18cm，BC=12cm，∴12×18•DE+12×12•DF=36，∴9DE+6DF=36．又∵DE=DF，∴9DE+6DE=36，∴DE=125...