Question:
Corresponding 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) 9 : 4
(d) 16 : 81
Solution:
If two triangles are similar, then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.
$\therefore \frac{\text { area of first triangle }}{\text { area of second triangle }}=\left(\frac{\text { Side of first triangle }}{\text { Side of second triangle }}\right)^{2}=\left(\frac{4}{9}\right)^{2}=\frac{16}{81}$
Hence, the correct answer is option (d)
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