Q. 254.5( 10 Votes )

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Answer :


Given: A ∆ABC with a point D on BC such that BD = DC


To prove: area(∆ABD) = x area(∆ABC)


Construction: Drop a perpendicular onto BC


Proof: area(∆ABC) = x BC x AE ---------------(1)


and, area(∆ABD) = x BD x AE ----------------- (2)


given that BD = DC ------------------ (3)


so, BC = BD + DC = BD + 2BD = 3BD [from 2]


BD = (BC)


Sub BD in (1), we get


area(∆ABD) = x ((BC) X AE)


area(∆ABD) = x ( BC X AE)


area(∆ABD) = x area(∆ABC) [from 1]


Hence proved


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