Question

D is a point on side AB of ABC, satisfying AD : BD = 1 : 2, If

DE || BC and AC = 12 cm, find the length of EC .​

Answer 1

Step-by-step explanation:

AD=23       [ Given ]

∴  DBAD+1=23+1

∴  DBAD+DB=23+2

∴  DBAB=25         --- ( 1 )

In △BDE and △ABC

∠B=∠B       [ Common ]

∠BAC=∠BDE        [ ∵DE∥AC ]

∴  △ABC∼△BDE    [ By AA similarity criteria ]

ar(△BDE)ar(△ABC)=DB2AB2=2252=425       [ From ( 1 ) ]

∴  ar(△ABC):ar(△BDE)=25:4