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Question

ABC and BDE are two equilateral triangles and BD = DC. Find the ratio between areas of ABC and BDE.
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Solution

In the given figure, it is given that ABC and BDF are equilateral triangles that is ABCBED and BD=DC.

We know that the area of similar triangles are proportional to squares of their corresponding altitude, therefore,

Ar(ABC)Ar(BDE)=BC2BD2

=(2BD)2BD2=4BD2BD2( BC=BD+DC,BD=DC)

=4

Hence the ratio between areas of ABC and BDE is 4:1.

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