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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:

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 4:1Given: △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)=BC2BD2A(△ABC)A(△BDE)=(2BD)2BD2 ....Since BC=2BDA(△ABC)A(△BDE)=4:1

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