In the adjoining figure,the point D divides the side BC of $△ A B C$ in the ratio m:n.Prove that $(△ A B D) : a r (△ A D C) = m : n$ .

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Solution

ar $(△ A B D)$ = ½ x B x H

= ½ x BD x AE

ar $(△ A D C)$ = ½ x B x H

= ½ x CD x AE

Now, their ratio :

½ x BD x AE/1/2 x CD x AE = BD/CD

Therefore BD/CD = BD : CD i.e m:n

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Similar questions

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In the adjoining figure,the point D divides the side BC of △ ABC in the ratio m:n.Prove that (△ ABD):ar(△ ADC)=m:n.

ar (△ ABD) = ½ x B x H = ½ x BD x AE ar(△ ADC) = ½ x B x H = ½ x CD x AE Now, their ratio : ½ x BD x AE/1/2 x CD x AE = BD/CD Therefore BD/CD = BD : CD i.e m:n

In the adjoining figure,the point D divides the side BC of $△ A B C$ in the ratio m:n.Prove that $(△ A B D) : a r (△ A D C) = m : n$ .

ar $(△ A B D)$ = ½ x B x H

= ½ x BD x AE

ar $(△ A D C)$ = ½ x B x H

= ½ x CD x AE

Now, their ratio :

½ x BD x AE/1/2 x CD x AE = BD/CD

Therefore BD/CD = BD : CD i.e m:n