In triangle ABC , if Ad divides BC in the ratio a:b ,then find ar(ABD):ar(ABC).

The figure according to question is shown below.


Let AM be the height (altitude) of the  ABC.
Area of a triangle = (12×base×height)

Now 
Area ABDArea ABC= (12×BD×AM)(12×BC×AM)                        = (BD)(BC) = (BD)(BD+DC)=a(a+b) (Ans)                          
 

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