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ABC and BDE are two equilateral triangles such that D is the midpoint of BC.Ratio of the areas of triangles ABC and BDE is

1376311_46099fabe6484661a008f27dd383aa11.PNG

A
2:1
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B
1:2
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C
4:1
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D
1:4
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Solution

The correct option is B 4:1
Given:ABC and BDE are equilateral.

BD=12BC as D is the midpoint of BC

Since ABC and BDE are equilateral.

Their sides would be in the same ratio

ABBE=ACED=BCBD

Hence by SSS similarity,ABCBDE

And, we know that the ratio of area of triangle is equal to the ratio of the square of corresponding sides.

So,areaofABCareaofBDE=BC2BD2

=BC2(BC2)2 since BD=BC2

=4BC2BC2

=41

Hence areaofABCareaofBDE=41

=4:1

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