Question

AABC and ABDE are two equilateral triangle such
that D is the mid-point of BC. Ratio of the areas of
triangles ABC and BDE is​

Answer 1

Answer:

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(△ABC)/A(△BDE) = BD²/BC²

A(△BDE)/A(△ABC) = (2BD)²/BD²

....Since BC=2BD

A(△BDE)/A(△ABC) =4:1

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