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State whether the following statement is true or false:

In the given figure, if $D$ and $E$ are two points on $BC$ such that $BD = DE = EC$ ,then $ar (Δ ABD) = ar (Δ ADE)$ $= ar (Δ AEC)$ .

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True

False

answer is A.

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Detailed Solution

Given that

D

and

E

are two points on

BC

such that

BD = DE = EC

Consider AP as the perpendicular to BC.
Area of triangle=

12

(base)(height)

⇒ a r Δ A B D = 12 B D A P ⇒ a r Δ A D E = 12 D E A P ⇒ a r Δ A E C = 12 E C A P

Since

B D = D E = E C

, and the triangles have the same height.
Therefore,

a r Δ A B D = a r Δ A D E = a r Δ A E C

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

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