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State true or false.

A point D is taken on the side BC of a ΔABC such that BD = 2DC. Then ar(ΔABD) = 2ar(ΔADC).

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True

False

answer is A.

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Detailed Solution

Given that in

Δ A B C,

B D = 2 D C

.
Draw a triangle ABC .
A point

D

is taken on side

B C

of triangle

A B C

such that

B D = 2 D C

.
Also take a point

E

as a midpoint on

B D

such that,

B E = E D

.
Therefore the figure will be,
Question Image

B E = E D

and

B D = 2 D C

.
Therefore,

B E = E D = D C

.
We know that, median of the triangle divides it into two equal triangles.
Here

A E a n d A D

are medians of

Δ A B D a n d Δ A E C

.
Therefore,

a r Δ A B D = 2 a r Δ A E D

……(1)
And

a r Δ A D C = a r Δ A E D

……(2)
Comparing (1) and (2), we get,

a r Δ A B D = 2 a r Δ A D C

Hence, the statement is true.
Therefore, option 1 is correct.

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