Solution: draw a picture according to the meaning of the question, as shown in the figure, let the waist length of an isosceles triangle AB=AC=2x, BC=y,

∫BD is the midline of the waist,

∴AD=DC=x，

If the length of AB+AD is 12cm, then 2x+x= 12 and x=4.

Then x+y= 15, that is, 4+y= 15, and the solution is y= 1 1.

The length of each side of the triangle is AB=AC=8cm, BC =11cm;

If the length of AB+AD is 15cm, then 2x+x= 15 and x=5.

Then x+y= 12, that is, 5+y= 12, and the solution is y = 7；;

At this time, the length of each side of the triangle is AB=AC= 10cm, BC=7cm.

So the answer is:

AB=AC=8cm, BC= 1 1cm or AB=AC= 10cm, BC=7cm.