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and are two equilateral triangles such that . Find the ratio of areas of aseminate and .

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2:1

4:1

1:1

1:2

answer is C.

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Detailed Solution

The area of the equilateral triangle

.
Where the sides of the equilateral triangle

.
It is given that

and

are two equilateral triangles such that

We need to find out the ratio of areas of the equilateral triangles

and

.
Since

is a equilateral triangle, thus we get

Let us take,

Also,

is a equilateral triangle, thus we get,

Let us take,

The area of the equilateral triangle

Also given that,

Therefore,

Therefore, the ratio of areas of the equilateral triangles

and

By using

we get,

Simplifying we get,

Hence

∴ The ratio of areas of the equilateral triangles

and

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