ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio ofthe areas of triangles ABC and BDE is

Question

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

Philoid · Accepted Answer

We know:

Equilateral triangles have all its angles as 60° and all its sides are of the same length. Therefore, all equilateral triangles are similar to each other.

Hence, the ratio between the areas of these triangles will be equal tothe square of the ratio between the sides of these triangles.

Let side of ΔABC = x

Therefore,

Side ofΔBDE =

Therefore,

)²

Hence, the correct answer is C

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

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

C. 4 : 1 D. 1 : 4