Solution: Because the perimeter of a triangle is the sum of three sides and the two sides of an isosceles triangle are equal, there are two situations:

1: When the side with the length of 38 is the waist with equal length, the side with equal length is also 38, leaving 92-38*2= 16.

2. When the side with a length of 38 is not equilateral, the waist length is (92-38)/2=27.