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

The perimeter of the 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 x denote the length of the first side of this triangle.

In the initial data for this task it is reported that this side is 8 centimeters shorter than the second side and 2 centimeters longer than twice the length of the third side, therefore, the length of the second side should be equal to x + 8 cm, and the length of the third side should be equal to (x – 2) / 2 cm.

Since the sum of the lengths of all sides of this triangle is 102 cm, therefore, we can draw up the following equation:

x + x + 8 + (x – 2) / 2 = 102,

solving which, we get:

2 * (x + x + 8 + (x – 2) / 2) = 2 * 102;

2 * (2x + 8 + (x – 2) / 2) = 204;

4x + 16 + x – 2 = 204;

5x + 14 = 204;

5x = 204 – 14;

5x = 190;

x = 190/5 = 38.

Find the lengths of the other two sides of the triangle:

x + 8 = 38 + 8 = 46;

(x – 2) / 2 = (38 – 2) / 2 = 36/2 = 18.

Answer: 38 cm, 46 cm and 18 cm.