Triangles ABC and A1B1C1 are similar. Perimeter A1B1C1 = 20 cm AB = 10, BC = 15, AC = 45. Find sides A1B1C1.

univerkov | April 21, 2021 | education

Let’s define the perimeter of the triangle ABC.

Ravs = AB + BC + AC = 10 + 15 + 45 = 70 cm.

The ratio of the perimeters of similar triangles is equal to the coefficient of similarity of these triangles.

K = Pa1v1s1 / Ravs = 20/70 = 2/7.

Then:

A1B1 / AB = 2/7.

A1B1 = AB * 2/7 = 10 * 2/7 = 20/7 = 2 (6/7) cm.

В1С1 = ВС * 2/7 = 15 * 2/7 = 30/7 = 4 (2/7) cm.

A1C1 = AC * 2/7 = 45 * 2/7 = 90/7 = 12 (6/7) cm.

Answer: The sides of triangle A1B1C1 are equal to 2 (6/7) cm, 4 (2/7) cm, 12 (6/7) 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.