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(A) 2 : 3

(B) 4 : 9

(C) 81 : 16

(D) 16 : 81

Answer :

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

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

\(\triangle\) ABC ~ \(\triangle\) DEF

And AB/DE = AC/DF = BC/EF = 4/9

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

Area(\(\triangle\) ABC)/Area(\(\triangle\) DEF) = \(AB^2/DE^2\)

Area(\(\triangle\) ABC)/Area(\(\triangle\) DEF) = \((4/9)^2\) = 16/81 = 16:81

Hence, the correct answer is (D).

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