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Question 4
Write True or False and justify your answer :
ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Then, ar (Δ BDE) = ar (Δ ABC).

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Solution

False.
Given,

Δ ABC and Δ BDE are two equilateral triangles.
Area of ΔABC=34×(side)2=34(BC)2
[ in equilateral Δ ABC, AB = BC = AC]
Given, D is the mid-point of BC.

BD=DC=12BC
Now, area of an equilateral ΔBDE=34×(side)2
=34×(BD)2
[ in equilateral Δ BDE, BD = DE = BE]
=34×(12BC)2
=34×14BC2=14×(34BC2)
Area of Δ BDE = 14 area of Δ ABC

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