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ABC and BDE are two equilateral triangles such that D is the midpoint of BC. Then, the ratio of area of triangle BDE to area of triangle ABC is:

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1: 2

1: 4

3: 2

3: 4

answer is B.

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Detailed Solution

Given ABC and BDE are two equilateral triangles such that D is the midpoint of BC.
Let all the sides of triangle ABC =

x

cm.
Now as D is midpoint,

B D = 12 B C

.
Sides of triangle BED =

x 2

cm.
Now area of triangle ABC is,

= 34 a 2

= 34 x 2

Now area of triangle BDE is,

= 34 a 2

= 34 x 2 2 = 34 × x 2 4

The ratio is,

= 34 x 2 34 × x 2 4 = 1 : 4

The ratio of area of triangle ABC to triangle BDE is 1: 4.
Hence, option 2 is correct.

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