The broken line consists of four links, the length of each next link is 6 cm longer

The broken line consists of four links, the length of each next link is 6 cm longer than the previous one. Find the length of each link of the polyline if it is known that the length of the polyline is 96 cm.

Let’s denote the length of the first link as x and write the expression for calculating the length of the polyline:

x + (x + 6) + (x + 6 + 6) + (x + 6 + 6 + 6) = 96.

Let’s simplify the left side of the expression:

x + x + 6 + x + 12 + x + 18 = 4x + 36.

Then we get the equation:

4x + 36 = 96,

x = (96 – 36): 4 = 15.

Therefore, the length of the first link is 15 cm, the second 21 cm, the third 27 cm, and the fourth 33 cm.