The side of the triangle is 5 cm, 6 cm, 7 cm, the perimeter of a similar triangle is 72 cm

The side of the triangle is 5 cm, 6 cm, 7 cm, the perimeter of a similar triangle is 72 cm, find the smaller side of the second triangle.

Similar triangles are triangles in which the angles are respectively equal, and the sides of one are respectively proportional to the sides of the other triangle.

In order to find the coefficient of similarity, which is equal to the ratio of the sides of these triangles, you need to find the ratio of their perimeters: PA1B1C1: PAVS.

To do this, we find the perimeter of the triangle ABC. The perimeter is the sum of all sides of the triangle:

P = AB + BC + AC;

P = 5 + 6 + 7 = 18 cm.

PA1B1C1: PAВС = 72/18 = 4;

A1B1: AB = B1C1: BC = A1C1: AC = 4;

A1C1 = AC ∙ 4;

В1С1 = ВС ∙ 4;

A1B1 = AB ∙ 4;

A1C1 = 5 ∙ 4 = 20 cm;

В1С1 = 6 ∙ 4 = 24 cm;

A1C1 = 7 ∙ 4 = 28 cm.

Answer: The length of the shorter side of the second triangle is 20 cm.