On the AB side of triangle ABC, point M is chosen so that AM: MB = 2: 7.

On the AB side of triangle ABC, point M is chosen so that AM: MB = 2: 7. Line MN is parallel to AC and intersects side BC at point N. Find the area of triangle ABC if the area of triangle MBN is 49

Since the problem is similar to triangles, then:
AM: MB = 2: 7, which means AB: MB = 9: 7.
The ratio of the areas of similar triangles is equal to the square of the coefficient of their similarity k ^ 2;
S triangle ABC: S triangle MBN = 81: 49.
The area of the triangle ABC refers to the area of the triangle MBN as 81: 49.
Triangle area MBN = 49
This means that the area of the triangle ABC = 81 ^ 2 centimeters.

Answer: the area of the triangle ABC = 81 ^ 2 centimeters.