Question

Abc and bde are two equilateral triangles such that bd=2/3bc find the ratio of triangles

Answer 1

Answer:

Step-by-step explanation:

In triangle ABC,

Since it is an equilateral traingle.

          AB =BC = AC

Also in triangle BDE,

 

               BD = DE = BE

Also it is given that,

                     BD = 2/3 BC

Also we know area of equilateral triangle 

     area = (root3/4) * a^2

      

in triangle ABC

          Area                          A1 = root3/4 * BC^2

Also, in triangle BDE,

                    Area                 A2 = root3/4 * BD^2

Ratio of the areas 

                          R = A1/A2

                          R = BC^2/BD^2

      Putting the value of BD

            

R = BC^2/ (2/3BC)^2

            R = 9/4

Thus the ratio of the areas of triangle to area of triangle BDE

R = 9:4