∆ABC and ∆BDE are two equilateral triangles such that D is the midpoint of BC. Then,

Question

∆ABC and ∆BDE are two equilateral triangles such that D is the midpoint of BC. Then, ar(∆BDE): ar(∆ABC) = ?

Philoid · Accepted Answer

Given: ∆ABC and ∆BDE are two equilateral triangles, D is the midpoint of BC.

Consider ΔABC

Here, let AB = BC = AC = x cm (equilateral triangle)

Now, consider ΔBED

Here,

BD = 1/2 BC

∴ BD = ED = EB = 1/2 BC = x/2 (equilateral triangle)

Area of the equilateral triangle is given by: (a is side length)

∴ ar(∆BDE): ar(∆ABC) = := :1 = 1:4