The sides of the triangle are 3cm, 4cm, 5cm. Find the smallest side of a similar triangle if its largest side is 2.5 cm.

A triangle is three points that do not lie on one straight line, connected by segments. In this case, the points are called the tops 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 triangle ΔABS is the side of the AC, which is 5 cm, then:

k = 2.5 / 5 = 0.5.

In order to calculate the length of the smallest side of the triangle ΔА1В1С1, you need to multiply the length of the corresponding side of the triangle ΔABS by the coefficient of similarity:

A1B1 = AB · k;

A1B1 = 3 0.5 = 1.5 cm.

Answer: the length of the smallest side A1B1 of the triangle ΔA1B1C1 is 1.5 cm.