Question

ABC and BDF are two equilateral triangles such that D is the midpoint of BC. Find the ratio of the areas of triangles ABC and BDE.

Answer 1

1/4 is the answer
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Answer 2

Step-by-step explanation:

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)

=

BD

2

BC

2

A(△BDE)

A(△ABC)

=

BD

2

(2BD)

2

....Since BC=2BD

A(△BDE)

A(△ABC)

=4:1

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