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

Question

Philoid · Accepted Answer

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

Since the given triangles are equilateral, they are similar triangles.

And also since D is the mid-point of BC, BD = DC.

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

∴ ar (ΔABC): ar (ΔBDE) = 4: 1