The line intersects the sides of triangle ABC at points M and K, respectively, so that MK is parallel to AC, BM: AM = 1: 4.

| June 20, 2021 | education

The line intersects the sides of triangle ABC at points M and K, respectively, so that MK is parallel to AC, BM: AM = 1: 4. Find the perimeter of triangle BMK if the perimeter of triangle ABC is 25 cm.

The aspect ratio BM: AM is 1: 4. Let BM be equal to x, then AM = 4x. Since AB = BM + AM, then AB = x + 4x = 5x.

Consider the triangles BMC and ABC: angle B is common for both triangles, the angle of BMC is equal to the angle BAC (corresponding angles with parallel MK and AC and secant AB).

So triangles BMK and ABC are similar.

Let’s calculate the coefficient of similarity:

k = AB / BM = 5x / x = 5.

This means that the perimeters are 5 to 1.

P (ABC) / P (BMK) = 5.

25 / R (BMK) = 5.

P (BMK) = 25/5 = 5 (cm).

Answer: The perimeter of the IUD triangle is 5 cm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.