Question

∆ABC and ∆BDE are two equilateral triangles such that D is the mid-point of BC. The ratio of the areas of triangle ABC and BDE is

(a) 2 : 1
(b) 1 : 2
(c) 4 : 1
(d) 1 : 4

Answer 1

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.



ΔABC and ΔBDE are equilateral triangles; hence they are similar triangles.

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.

Hence the correct answer is .