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 ΔBDE 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 ΔBDE, BD = DE = BE] =√34×(12BC)2 =√34×14BC2=14×(√34BC2)
Area of Δ BDE = 14 area of Δ ABC