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).