Question

In the given figure in ∆ABC point D is on side AC of AC=16, DC=9 and BP perpendicular AC then find the following ratios 1) A(∆ABD)/A(∆ABC) 2) A(∆BDC)/A(∆ABC) 3) A(∆ABD)/A(∆BDC)​

Answer 1

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