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Relation between Areas and Sides of Similar Triangles

If Δ ABC and ...

Question

If $Δ A B C$ and $Δ B D E$ are equilateral triangles, where D is the mid point of BC, find the ratio of areas of $Δ A B C$ and $Δ B D E$

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Solution

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

To find:
Ar

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

s

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