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Tell whether the following statement is true or false:

Triangles ABC and BDE are two equilateral triangles such that DE is the midpoint of BC. Then area of triangle BDE = $14$ area of triangle ABC.

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True

False

answer is A.

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Detailed Solution

Given triangles ABC and BDE are two equilateral triangles such that DE is the midpoint of BC.
Question Image

As, triangles ABC and BDE are two equilateral triangles
Area of equilateral triangle ABC is,

= 34 × s i d e 2

As, all sides are equal

= 34 × B C 2

Now,
BD = DC =

12

BC
Area of equilateral triangle BDE is,

= 34 × B D 2 = 34 × 12 B C 2 = 34 × 14 B C 2 = 14 × 34 B C 2

Area of triangle BDE =

14

Area of triangle ABC.
Given statement is true.
Hence, option 1 is correct.

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