in the a triangle AD=2 AND DB =3 IF DE=4, if DE || BC, then BCequals
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Answer:
AD
=
2
3
[ Given ]
∴
DB
AD
+1=
2
3
+1
∴
DB
AD+DB
=
2
3+2
∴
DB
AB
=
2
5
--- ( 1 )
In △BDE and △ABC
∠B=∠B [ Common ]
∠BAC=∠BDE [ ∵DE∥AC ]
∴ △ABC∼△BDE [ By AA similarity criteria ]
ar(△BDE)
ar(△ABC)
=
DB
2
AB
2
=
2
2
5
2
=
4
25
[ From ( 1 ) ]
∴ ar(△ABC):ar(△BDE)=25:4
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