Question

Traingle abc and triangle bde are two equilateral traingles such that d is the mid point of bc find the ratio of the areas of triangles abc and bde

Answer 1

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

hope this helps

#bebrainly

Answer 2

Answer:

Given:

• ΔABC and ΔBDE are two equilateral triangles such that D is the midpoint of BC.

To find:

• Ratio of areas of ΔABC and ΔBDE.

Solution :

Since D is the midpoint of BC, BD = DC.

We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.