AD=CD is known, so AB-BC= 15-6=9.

Let BC=X, then AB=AC=X+9.

It is known that the L triangle ABC= 15+6=2 1, so X+2(X+9)=2 1, then X= 1, and X+9= 10. That is AB=AC= 10, BC= 1.

So the waist length of the triangle is 10, and the base length is 1.

Suppose AB+AD=6, BC+CD= 15.

AD=CD is known, so BC-AB= 15-6=9.

Let AB=Y, then BC=Y+9.

Given that l triangle ABC= 15+6=2 1, so Y+9+2Y=2 1, then Y=4, Y+9= 13. That is AB=AC=4, BC= 13.

Because the sum of two sides of the triangle is greater than the third pass and 4+4 is less than 13, the triangle is not established.