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Question

In △ ABC, D is a point on BC such that BD: DC = 1 : 2. If area △ ADC = 45 sq cm, then area of △ ABD = ____ sq cm.


  1. 20

  2. 22.5

  3. 45

  4. 90


Solution

The correct option is B

22.5


We know that if a line from a vertex of a triangle to its opposite side divides that side in the ratio 1:2, then the area of this triangle is also divided in the same ratio.
i.e.,  
If BD:DC=1:2, then area (ABD) : area (ADC) = 1:2
Given, area (ADC) = 45 sq. cm, we must have area (ABD) = 22.5 sq. cm.

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