Triangle ABC has points D and E on sides AB and AC respectively of the triangle such that area(∆DBC) = area(∆EBC). Then which of the following options is correct?

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DE || BC.

AD || BE

DB || EC

None of the above

answer is A.

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Detailed Solution

Given that, triangle ABC has points D and E on sides AB and AC respectively of the triangle such that area(∆DBC) = area(∆EBC).
The following figure depicts the given situation.
Question Image

From the figure, we get that

Δ B D C and Δ B E C

have the same base BC and lie between the lines DE and BC.
We are also given that

a r (Δ B D C) = a r (Δ B E C)

.
The above condition is only possible when the triangles lie between the same parallel lines. So, DE has to be parallel to BC.
Thus, DE||BC if

a r (Δ B D C) = a r (Δ B E C)

.
Therefore, the correct option is 1.

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