I have been given a simple homework assignment from kid in my family and do not know how to help him. I am pretty sure that there problem is unsolvable in its current state and he forgot some additional information. Please correct me if Im wrong:
"We are given a isosceles triangle ABC, where AB=BC. On the line of AB, but not within AB, at the side of B, there is a point D. Now D is connected to B and C and we get new triangle - ADC. What is the length of AC, given that we know the perimeters: ABC, ADC ?"
You're correct: the problem as stated is not soluble.
Proof: Suppose the perimeter of ABC is 10 and the perimeter of ADC is 20.
Solution 1: AC=2, BC=AB=4, D chosen along line of AB so that BD+DC = 10.
Solution 2: AC=4, BC=AB=3, D chosen along line of AB so that BD+DC = 10.
The solutions are both correct and give different values for AC.