Question

If the sides of two similar triangles are in the ratio $2:3$, then their areas are in the ratio

• A. $9:4$
• B. $4:9$
• C. $2:3$
• D. $3:2$

Answer 1

The correct option is B $4:9$

Let $ABC$ and $DEF$ be two similar triangles.

Then, $\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}=\frac{2}{3}$ ....Given

Therefore, $\frac{Area\left(ABC\right)}{Area\left(DEF\right)}=\frac{A{B}^2}{D{E}^2}$ ....The ratio of areas of these triangles will be equal to the square of the ratio of the corresponding sides

$\Rightarrow \frac{Area\left(ABC\right)}{Area\left(DEF\right)}={\left(\frac{2}{3}\right)}^2=\frac{4}{9}$

Hence, their areas are in the ratio of $4:9$.

Therefore, option B is correct.