Explanation:

- We have triangle ABC with DE parallel to BC.

- Given that AD : DB = 7 : 9.

- This uses the basic proportionality theorem (also known as Thales's theorem).

- The theorem states that if a line is drawn parallel to one side of a triangle, it divides the other two sides in the same ratio.

- Thus, DE divides triangle ABC into two smaller triangles, DEF and CBF, both similar to triangle ABC.

- For similar triangles, the ratio of their areas is the square of the ratios of their corresponding sides.

- Here, (AD/DB)^2 = (7/9)^2, which is 49/81.

- Triangle DEF corresponds to triangle ABC in this ratio: 49 parts and triangle CBF to ABC as 81 parts.

- The ratio of areas is therefore 49 : 81.

- Option 2: 49 : 81 is the correct answer.

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