The perimeter of a triangle is 102 cm, one side is 8 cm shorter than the other and its length is 2 cm

The perimeter of a triangle is 102 cm, one side is 8 cm shorter than the other and its length is 2 cm more than twice the length of the third side. Find the lengths of the sides of the triangle.

Let’s solve this problem using the equation.
Let x centimeters be the third side of the triangle, then the first side is (2 * x + 2) centimeters, and the second side is (2 * x + 2 + 8) centimeters. We know that the perimeter of the triangle is 102 centimeters. Let’s make the equation:
x + 2 * x + 2 + 2 * x + 2 + 8 = 102;
x + 2 * x + 2 * x + 12 = 102;
x + 2 * x + 2 * x = 102 – 12;
x + 2 * x + 2 * x = 90;
x * (1 + 2 + 2) = 90;
x * (3 + 2) = 90;
x * 5 = 90;
x = 90: 5;
x = 18 centimeters – the length of the third side;
18 * 2 + 2 = 38 centimeters – the length of the first side;
38 + 8 = 46 centimeters – the length of the second side.
Answer: 38 centimeters; 46 centimeters; 18 centimeters.