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

Answer 1

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