[16 : 81] Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio

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Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio

2 : 3

4 : 9

81 : 16

16 : 81

Explanation:

Given, Sides of two similar triangles are in the ratio 4 : 9

Let ABC and DEF are two similar triangles, such that,

ΔABC ~ ΔDEF

And $\dfrac{AB}{DE} = \dfrac{AC}{DF} = \dfrac{BC}{EF} = \dfrac{4}{9}$

As, the ratio of the areas of these triangles will be equal to the square of the ratio of the corresponding sides,

$\dfrac{ Area(ΔABC)}{Area(ΔDEF)} = \dfrac{AB^2}{DE^2}$

$\dfrac{ Area(ΔABC)}{Area(ΔDEF)} = (\dfrac{4}{9})^2 = \dfrac{16}{81}$ = 16:81

Hence, the correct answer is (D)

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