Point M is taken on the side AC of triangle ABC, and AM: NC = 2: 7. Find the area of triangle MBC

univerkov | May 18, 2021 | education

Point M is taken on the side AC of triangle ABC, and AM: NC = 2: 7. Find the area of triangle MBC if the area of triangle ABC is 72 cm2.

Let the length of the segment AM = 2 * X cm, then the length of the segment MC = 7 * X cm.

Side length AC = AM + CM = 2 * X + 7 * X = 9 * X cm.

Triangles ABC and BMC have the same height ВН, drawn to the sides of AC and CM, then the ratio of the areas of the triangles is equal to the ratio of the lengths of the sides to which the height is drawn.

Savs / Smvs = AC / CM.

Smvs = Savs * CM / AC = 72 * 7 * X / 9 * X = 56 cm2.

Answer: The area of the MBC triangle is 56 cm2.

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