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Question

In triangle ABC, D is a point on side BC such that 2BD = 3DC. Which of the following option is correct?


A

Area of triangle ABD = Area of triangle ABC

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B

Area of triangle ABD = Area of triangle ABC

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C

Area of triangle ABD = Area of triangle ABC

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D

Area of triangle ABD = Area of triangle ABC

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Solution

The correct option is C

Area of triangle ABD = Area of triangle ABC


2BD = 3DC

BDDC=32BD(BD+DC)=3(3+2)BDBC=35

Since, Δ ABD and Δ ABC have the same vertex A and their bases along the same straight line BC, the areas of the triangles are in the ratio of their bases.

Area of Δ ABDArea of Δ ABC=BDBC=Area of Δ ABDArea of Δ ABC=35Area of Δ ABD=35 Area of Δ ABC


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