Triangles ABC and MNK are similar. AB = 2cm, BC = 4cm, AC = 5cm, MK = 10cm. Find the perimeter of the triangle MNK.

The ratio of the respective sides of such triangles is called the coefficient of similarity – it shows how many times the side of one triangle is larger than the corresponding side of the other. Let’s find the coefficient of similarity:

k = MK / AC = 10/5 = 2.

Let’s find the unknown sides of the triangle MNK by multiplying the corresponding sides of the triangle ABC by the coefficient of similarity:

MN = AB * 2 = 2 * 2 = 4 cm;

NK = BC * 2 = 4 * 2 = 8 cm.

Find the perimeter of the triangle MNK by adding its sides:

P = MK + MN + NK = 10 + 4 + 8 = 22 cm.

Answer: 22 cm