The corresponding sides of two similar triangles are in the ratio of 2 : 3. If the areas of the smaller triangle is 36 sq cm, then the area of the bigger triangle is:

Correct option is C

Given:
The ratio of corresponding sides of two similar triangles is 2:3, and the area of the smaller triangle is 36 sq cm.
Formula Used:
For two similar triangles, the ratio of their areas is the square of the ratio of their corresponding sides:
​$$\frac{\text{Area of smaller triangle}}{\text{Area of bigger triangle}} = \left(\frac{\text{Side of smaller triangle}}{\text{Side of bigger triangle}}\right)^2$$​​
Solution:
 Let the area of the bigger triangle be X.
​$$\frac{36}{X} = \left(\frac{2}{3}\right)^2\\\\\frac{36}{X} = \frac{4}{9}\\36 \times 9 = 4 \times X\\324 = 4X\\X = \frac{324}{4} = 81$$​​
Thus, the area of the bigger triangle is 81 sq cm.