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Sides of two similar triangles are in the ratio $4 : 9$ , areas of these triangles are in the ratio

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2 : 3

4 : 9

81 : 16

16 : 81

answer is D.

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Detailed Solution

Given that sides of two similar triangles are in the ratio

4 : 9

.
Let

S_{1}

and

S_{2}

be the sides of similar triangles.
Also,

A_{1}

and

A_{2}

be the areas of similar triangles.
As,

\frac{S_{1}}{S_{2}} = \frac{4}{9}

For Similar triangles, the ratio of the areas of two similar triangles is equal to the square of the ratio of any pair of their corresponding sides.

\Rightarrow \frac{A_{1}}{A_{2}} = \frac{(S_{1})^{2}}{(S_{2})^{2}}

\Rightarrow \frac{A_{1}}{A_{2}} = \frac{4^{2}}{9^{2}}

\Rightarrow \frac{A_{1}}{A_{2}} = \frac{16}{81}

Therefore,

\frac{A_{1}}{A_{2}} = \frac{16}{81}

.
So, the area of the triangles are in the ratio 16:81.
Hence option 4 is the answer.

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