1. If the adjoining figure, D divides AB such that DB: AD = 3:2 and E is a point on AC such that DE II BC. Find the ration of areas of triangle ABC and triangle ADE
a) 25:4
b) 2:5
c) 4:25
d) 5:2
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DB
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
solution
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