Understand the Theorem of Areas of Similar Triangles

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

$\frac{\text{Area}_1}{\text{Area}_2} = \left(\frac{\text{Side}_1}{\text{Side}_2}\right)^2$

Substitute the Given Values

Given that the ratio of the corresponding sides is $2:3$ and the area of the smaller triangle is $36\text{ sq cm}$.

$\frac{36}{\text{Area}_\text{bigger}} = \left(\frac{2}{3}\right)^2$

Calculate the Area of the Bigger Triangle

Squaring the ratio gives $\frac{4}{9}$. Therefore, $\frac{36}{\text{Area}_\text{bigger}} = \frac{4}{9}$.

$\text{Area}_\text{bigger} = \frac{36 \times 9}{4} = 9 \times 9 = 81\text{ sq cm}$