@mmk2015 estimation sometimes works, and it may be a good strategy for certain people or for specific problems, but by estimating it’s often difficult to ascertain whether the answer is correct. You said that the two belt lengths have length roughly 8, but in fact their length must be less than 8.
Note that this problem was solved using very little math - only some drawing/constructing segments and noticing a 30-60-90 triangle. The hard part was explaining the solution without a diagram.