Tick the correct answer and justify:
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
Let ABC and DEF are two similarity triangles ΔABC ~ ΔDEF (Given)
and, AB/DE = AC/DF = BC/EF = 4/9 (Given)
∴ area(ΔABC)/area(ΔDEF) = AB2/DE2 [the ratio of the areas of these triangles will be equal to the square of the ratio of the corresponding sides]
∴ area(ΔABC)/area(ΔDEF) = (4/9)2 = 16/81 = 16:81
Hence, the correct option is (D).
