Q. 16

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

ar(∆BDE): ar(∆ABC) = ?


A. 1:2

B. 1:4

C. 3:2

D. 3:4

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

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