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# Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio (A) 2 : 3 (B) 4 : 9 (C) 81 : 16 (D) 16 : 81

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).