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State true or false.

In the following figure, $D$ and $E$ and are two points on $B C$ are two points on such that $B D = D E = E C$ such that . Then that $a r Δ A B D = a r Δ A D E = a r Δ A E C$ . Then that .

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True

False

answer is A.

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Detailed Solution

Given that, the figure.
Question Image

D

and

E

are two points on

B C

such that

B D = D E = E C

.
Draw

A M ⊥ B C

Since,
Area of the triangle

= 12 × b a s e × h e i g h t

Then,
Area of

Δ A D E = 12 × D E × A M

,
Area of

Δ A B D = 12 × B D × A M

,
Area of

Δ A E C = 12 × E C × A M

We know that,

B D = D E = E C

⇒ 12 × D E × A M = 12 × B D × A M = 12 × E C × A M

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

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

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