If $$\triangle ABC \sim \triangle DEF, AB = 4\ cm, DE = 6\ cm, EF = 9\ cm$$ and $$FD = 12\ cm$$, then find the perimeter of $$\triangle ABC$$.

As per the dimensions give in the questions,
Now, we have to find out the perimeter of $$\triangle ABC$$
Let $$\triangle ABC \sim \triangle DEF$$
So, $$AB/DE = AC/DF = BC/EF$$
Consider, $$AB/DE = AC/DE$$
$$4/6 = AC/12$$
By cross multiplication we get,
$$AC = (4 \times 12)/6$$
$$AC = 48/6$$
$$AC = 8 cm$$
Then, consider $$AB/DE = BC/EF$$
$$4/6 = BC/9$$
$$BC = (4 \times 9)/6$$
$$BC = 36/6$$
$$BC = 6 cm$$
Therefore, the perimeter of $$\triangle ABC = AB + BC + AC$$
$$= 4 + 6 + 8$$
$$= 18 cm$$.