# The sides of the triangle are 6cm, 3cm, 7cm. Find the perimeter of a triangle similar to this one if its largest side is 56cm.

A triangle is three points that do not lie on one straight line, connected by segments. In this case, the points are called the vertices of the triangle, and the segments are called its sides.

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 length of the sides of a triangle ΔА1В1С1 similar to this one, you need to find the coefficient of similarity of these triangles. The similarity coefficient is the number k equal to the ratio of the similar sides of similar triangles:

k = A1B1 / AB = B1C1 / BC = A1C1 / AC.

Since the largest side of the ΔABS triangle is the AC side, which is 7 cm, then

k = A1C1 / AC;

k = 56/7 = 8.

Find the remaining sides of the triangle ΔА1В1С1. To do this, we multiply the length of the corresponding sides of the triangle ΔABS by the coefficient of similarity:

A1B1 = AB ∙ k;

A1B1 = 6 8 = 48 cm;

В1С1 = ВС ∙ k;

В1С1 = 3 ∙ 8 = 24 cm.

The perimeter of a triangle is the sum of all its sides:

P1 = A1B1 + B1C1 + A1C1;

Р1 = 48 + 24 + 56 = 128 cm.

Answer: the perimeter of the triangle ΔА1В1С1 is 128 cm.