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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

9:16

16:81

answer is D.

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Detailed Solution

It is given that sides of two similar triangles are in the ratio 4:9 and we need to find the ratio of areas of these triangles.

It is known that for two similar triangles, the ratio of the areas of the triangle will be equal to the square of the ratio of the sides of the triangles. Therefore, the ratio of areas is given by ${(\frac{4}{9})}^{2}$ .

Hence, the ratio of areas is $\frac{16}{81}$ or 16:81.

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