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Tell whether the following statement is true or false:

In triangle ABC, it given that D is the midpoint of BC, E is the midpoint of BD and O is the midpoint of AE. Then area of triangle BOE is $18 ×$ area of triangle ABC.

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True

False

answer is A.

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Detailed Solution

Given a triangle ABC.
In Δ ABC , it is given that D is the midpoint of BC, E is the midpoint of BD and O is the midpoint of AE. Then ar( Δ BOE ) = ?

As, AD is median of triangle ABC,
Area of triangle ABD = Area of triangle ADC
Area of triangle ABD =

12 ×

Area of triangle ABC
Now, AE is median of triangle ABD,
Area of triangle ABE = Area of triangle AED

⇒

Area of triangle ABE =

12 ×

Area of triangle ABD

Area of triangle ABE =

12 × 12 ×

Area of triangle ABC

⇒

Area of triangle ABE =

14 ×

Area of triangle ABC
Now, BO is median in triangle ABE,
Area of triangle BOE = Area of triangle AOB

⇒

Area of triangle BOE =

12 ×

Area of triangle ABE

⇒

Area of triangle BOE =

12 × 14 ×

Area of triangle ABC

⇒

Area of triangle BOE =

18 ×

Area of triangle ABC
Given statement is true.
Hence, option 1 is correct.

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Tell whether the following statement is true or false:In triangle ABC, it given that D is the midpoint of BC, E is the midpoint of BD and O is the midpoint of AE. Then area of triangle BOE is 1 8 × area of triangle ABC.

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Tell whether the following statement is true or false:

In triangle ABC, it given that D is the midpoint of BC, E is the midpoint of BD and O is the midpoint of AE. Then area of triangle BOE is $18 ×$ area of triangle ABC.