The sides of a triangle are 4, 7 and 8. Find the sides of a similar triangle with P = 57.

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.

To do this, find the ratio of the perimeters of these triangles:

k = P1 / P;

P = AB + BC + AC;

P = 4 + 7 + 8 = 19 cm;

k = 57/19 = 3.

Thus:

A1B1 = AB · k;

A1B1 = 4 3 = 12 cm;

В1С1 = ВС · k;

B1C1 = 7 3 = 21 cm;

A1C1 = AC · k;

A1C1 = 8 3 = 24 cm.

Answer: the sides of the half-length triangle ΔА1В1С1 are 12 cm, 21 cm, 24 cm.