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Question

ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the area of triangles ABC and BDE is


A

2:1

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B

1:2

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C

4:1

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D

1:4

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Solution

The correct option is C

4:1


As ∆ABC and ∆EBD are equilateral triangles, it means all the angles are equal in both the triangles i.e. 600.

Therefore, by AA similarity criteria, we can say that,

∆ABC∼∆EBD

Now, the triangles are similar, it means,

Area(ABC)Area(EBD)=BC2BD2

Let the length of each side of ∆ABC is 2x.

D is the midpoint of BC, it means

BD=DC=12BC

BD=12×2x=x

Therefore,

Area(ABC)Area(EBD)=BC2BD2=(2x)2x2=4x2x2=41=4:1

Hence, option C is the correct option.


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