Question

如图,已知BD是∠ABC的角平分线,DE⊥AB与E,S△ABC=36cm²;,AB=18cm,则DE=

Answer 1

∵BD是∠ABC的角平分线,DE⊥AB,DF⊥BC,

∴DE=DF,

∵S△ABC=36cm2,S△BCD=1/2BC•DF,

又∵S△ABC=S△ABD+S△BCD,AB=18cm,BC=12cm,

∴1/2×18DE+1/2×12DF=36,

∴9DE+6DF=36．

又∵DE=DF,

∴9DE+6DE=36,

∴DE=12/5cm．