In the adjoining figure, the points D divides the

Side BC of ∆ABC in the ratio m:n. prove that area(∆ABD): area(∆ABC) = m:n


Given : A ∆ABC in which a point D divides the Side BC in the ratio m:n.


To prove: area(∆ABD): area(∆ABC) = m:n


Construction : Drop a perpendicular AL on BC


Proof:


area(∆ABD) = x BD x AL ---------------- (1)


and, area(∆ADC) = x DC x AL ------------------ (2)


BD:DC = m:n



--------------(3)


sub Eq (3) in eq (1)


area(∆ABD) = x ( x DC) x AL


area(∆ABD) = x ( x DC x AL)


area(∆ABD) = x area(∆ADC)


=


Area(∆ABD): Area(∆ABC) = m:n


Hence proved


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