Question

If ∆ABC and ∆BDE are equilateral triangles, where D is the mid point of BC, find the ratio of areas of ∆ABC and ∆BDE.

Answer 1

Given: In ΔABC and ΔBDE are equilateral triangles. D is the midpoint of BC.

To find: $\frac{\mathrm{Ar}\left(∆\mathrm{ABC}\right)}{\mathrm{Ar}\left(∆\mathrm{BDE}\right)}$

In ΔABC and ΔBDE

Since D is the midpoint of BC, BD : DC = 1.

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

Let DC = x, and BD = x

Therefore BC = BD + DC = 2x

Hence