Problem of the Week

Problem D

Different Lengths

$$\triangle ABC$$ is isosceles with $$AB=AC$$. All three side lengths of $$\triangle ABC$$ and also altitude $$AD$$ are positive integers.
If the area of $$\triangle ABC$$ is 60 cm$$^2$$, determine all possible perimeters of $$\triangle ABC$$.

Note: You may use the fact that the altitude of an isosceles triangle drawn to the unequal side bisects the unequal side.