The perimeter of a triangle is 70 cm. Find the lengths of the sides of this triangle if AB refers to BC

The perimeter of a triangle is 70 cm. Find the lengths of the sides of this triangle if AB refers to BC as 3: 4, and BC refers to AC as 6: 7.

Let the proportionality coefficient be x cm, then the lengths of the sides of the triangle ABC will be: AB = 3 ∙ x cm, and BC = 4 ∙ x cm, since it is known from the condition of the problem that AB and BC are related as 3: 4.On the other hand, BC refers to AC as 6: 7, which means AC = BC: 6/7 = 4 ∙ x ∙ 7/6 = (14/3) ∙ x (cm). Knowing that the perimeter of the triangle is 70 cm, we compose the equation:

3 ∙ x + 4 ∙ x + (14/3) ∙ x = 70;

x = 6 (cm);

AB = 3 ∙ 6 = 18 (cm);

BC = 4 ∙ 6 = 24 (cm);

AC = (14/3) ∙ 6 = 28 (cm).

Answer: 18 cm, 24 cm, 28 cm are the lengths of the sides of this triangle.