Explanation:

- Perimeters and Similar Triangles: When triangles are similar, the ratio of their perimeters is equal to the ratio of their corresponding sides.

- Given Ratios of Perimeters: The perimeter ratio is 36 cm to 24 cm. Simplifying this gives:

$$

\frac{36}{24} = \frac{3}{2}

$$

- Area Ratio: For similar triangles, the ratio of their areas is the square of the ratio of their corresponding sides (or perimeters).

- Calculating Area Ratio:

$$

\left(\frac{3}{2}\right)^2 = \frac{9}{4}

$$

- Option Analysis:

- Option 1: 6 : 13 - This option does not match our calculations.

- Option 2: 2 : 3 - This option is incorrect based on perimeter square rule.

- Option 3: 9 : 4 - This option matches our calculated area ratio.

- Option 4: 35 : 24 - This option does not coincide with computations.