In the triangle ABC, AB = AC, the middle line BD of AC, divide the triangle ABC into two parts with perimeters of 12cm and 15cm respectively, and find the respective lengths of the triangle ABC.

BD is the AC center line.

∴AD=AC

Let AD be X, then DC is X and AB is 2x.

Such as AB+AD= 12cm, BC+CD= 15cm.

2x+x= 12

x+y= 15

x=4 y= 1 1

∴AB=AC=8,BC= 1 1

Such as AB+AD= 15cm, BC+CD= 12cm.

2x+x= 15

x+y= 12

x=5，y=7

∴AB=AC= 10,BC=7

There are two answers, and the process is clear. BD is not included in O (∩ _ ∩) O.