Question

ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of
areas of triangles ABC and BDE is
(A) 2:1
(B) 1:2
(C) 4:1
(D) 1:4​

Answer 1

Answer:

it is (c) 4:1

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