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Question

ABC and BDE are two equilateral triangles such that D is the midpoint of BC. Ratio of A(ABC) and A(BDE) is:
235416_b53b46d6261e451a8d88eead47f1187d.png

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

Given: ABC and BDE are equilateral triangles.
D is midpoint of BC.
Since, ABC and BDE are equilateral triangles.

All the angles are 60 and hence they are similar triangles.
Ratio of areas of similar triangles is equal to ratio of squares of their sides:

Now, A(BDE)A(ABC)=BC2BD2

A(ABC)A(BDE)=(2BD)2BD2 ....Since BC=2BD

A(ABC)A(BDE)=4:1


233106_235416_ans.PNG

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