Question

ABC and BDE are two equilateral triangle such that D is the mid-point of bc. ratio of areas of triangle ABC and BDE is
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Answer 1

Answer:

ABC and BDE are two equilateral triangles such that D is the mid point of BC. What is ar (ABC) : ar (BDE)?

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ABC and BDE are two equilateral triangles such that D is the mid point of BC. What is ar (ABC) : ar (BDE)?

We know that area( equilateral triangle)= √3a²/4 , where a is the side of the triangle.

If each side of tri ABC = 2a unit

Then, Area (triABC) = √3 a² ……….. (1)

Now, BD = BC/2 ( given)

=> BD = 2a/2 = a

So, area( equilateral triangle BDE)=√3a²/4 ….(2)

By dividing (1) by (2)

ar( tri ABC) / ar(tri BDE) = (√3a²*4)/ √3a² = 4/1

= 4 : 1