question_answer

ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is:                                                                                                                (NCERT EXERCISE)

A) \[2:1\]

B) \[1:2\]

C) \[4:1\]

D) \[1:4\]

Correct Answer: C

Solution :

[c] Since ABC and BDE are two equilateral triangles

\[\therefore \,\,\,\,\,\,\,\,\frac{ar(\Delta ABC)}{ar(\Delta BDE)}=\frac{\sqrt{3}/4{{a}^{2}}}{\sqrt{3}/4\,{{(a/2)}^{2}}}=\frac{4}{1}\]