Question

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

Answer 1

ΔABC and ΔBDE are two equilateral triangle such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is 4 : 1.

Explanation:

`(ar(ΔABC))/(ar(ΔBDE)) = (sqrt(3)/4 (BC)^2)/(sqrt(3)/4 (BD)^2)`

= `(BC)^2/(((BC))/2)^2`

= `(4BC^2)/(BC^2)`

= `4/1`

= 4 : 1