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
• B. Area of triangle ABD = Area of triangle ABC
• C. Area of triangle ABD = Area of triangle ABC
• D. Area of triangle ABD = Area of triangle ABC

Answer 1

The correct option is C

Area of triangle ABD = Area of triangle ABC

2BD = 3DC

$\frac{BD}{DC}=\frac{3}{2}\frac{BD}{(BD+DC)}=\frac{3}{(3+2)}\frac{BD}{BC}=\frac{3}{5}$

Since, $\Delta$ ABD and $\Delta$ 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.

$\frac{Areaof\Delta ABD}{Areaof\Delta ABC}=\frac{BD}{BC}=\frac{Areaof\Delta ABD}{Areaof\Delta ABC}=\frac{3}{5}Areaof\Delta ABD=\frac{3}{5}Areaof\Delta ABC$