The perimeter of a triangle ABC is 68 cm.Find the lengths of the sides of this triangle if AB: BC = 2: 3 and BC: AC = 6: 7

We denote by the unknown variable x centimeters – the length of the side AB,

Then AB: BC = 2: 3, BC = 3/2 * AB = 3/2 * x centimeters – the length of the BC side,

Then BC: AC = 6: 7, AC = 7/6 * BC = 7/6 * 3/2 * x = 7/4 * x centimeters – the length of the AC side.

By the condition of the problem, the perimeter of the triangle is 68 centimeters. Let’s make the equation:

x + 3/2 * x + 7/4 * x = 68;

17/4 * x = 68;

x = 16 centimeters – the length of the AB side,

3/2 * 16 = 24 centimeters – the length of the BC side,

7/4 * 16 = 28 centimeters – the length of the BC side.