Question

Question 9
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

Answer 1

(D) 16 : 81


Let ABC and DEF are two similar triangles.
i.e; $\Delta ABC\sim \Delta DEF$ (Given)
$\frac{AB}{DE}=\frac{AC}{DF}=\frac{BC}{EF}=\frac{4}{9}$ (Given)
Since the ratio of the areas of these triangles will be equal to the square of the ratio of the corresponding sides.
$\frac{area\left(\Delta ABC\right)}{area\left(\Delta DEF\right)}=\frac{A{B}^2}{D{E}^2}$
$\therefore \frac{area\left(\Delta ABC\right)}{area\left(\Delta DEF\right)}=(\frac{4}{9}{)}^2=\frac{16}{81}=16:81$