Question

Sides of two similar triangles are in the ratio of 4: 9. Areas of these triangles are in the ratio?

• A. 2:3
• B. 4:9
• C. 81:16
• D. 16:81

Answer 1

The correct option is D

16:81

As we know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
Let ABC and DEF are two triangles.
Then, $\frac{areaof\left(△ABC\right)}{areaof\left(△DEF\right)}=\frac{A{B}^2}{D{E}^2}={\left(\frac{4}{9}\right)}^2=\frac{16}{81}$
Therefore, areas of these triangles are in the ratio 16:81.