Question

If ABC and BDE are two equilateral triangles such that D is the mid-point of BC, then find ar(△ABC) : ar(△BDE).

Answer 1

Given: ABC and BDE are two equilateral triangles.

We know, area of an equilateral triangle = √3/4 (side)²

Let “a” be the side measure of given triangle.

Find ar(△ABC):

ar(△ABC) = √3/4 (a)²

Find ar(△BDE):

ar(△BDE) = √3/4 (a/2)²

(D is the mid-point of BC)

Now,

ar(△ABC) : ar(△BDE)

or √3/4 (a)² : √3/4 (a/2)²

or 1 : 1/4

or 4:1

This implies, ar(△ABC) : ar(△BDE) = 4:1

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Answer 2

Answer:

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Step-by-step explanation:

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