To find the perimeter of the triangle, we simply add the lengths of all three sides. The side lengths are given as:

1. $(r - 10s)$ cm
2. $(3r + 2t)$ cm
3. $(2t - 6s)$ cm

The perimeter $P$ of the triangle is the sum of these side lengths:

$P = (r - 10s) + (3r + 2t) + (2t - 6s)$

Now, let's combine like terms:

1. For $r$-terms: $r + 3r = 4r$
2. For $s$-terms: $-10s - 6s = -16s$
3. For $t$-terms: $2t + 2t = 4t$

So, the perimeter expression simplifies to:

$P = 4r - 16s + 4t$

Thus, the expression for the perimeter of the triangle is:

$P = 4r - 16s + 4t$

Would you like to go into more detail, or do you have any further questions?

Here are 5 related questions to explore this topic further:

1. What are the properties of a triangle with variable side lengths?
2. How do you solve for the perimeter if the values of $r$, $s$, and $t$ are known?
3. Can you use this formula to determine if the triangle is valid for certain values of $r$, $s$, and $t$?
4. How would you calculate the area of this triangle if you knew its height?
5. What happens to the perimeter if one of the side lengths changes proportionally?

Tip: Always remember to simplify expressions by combining like terms to avoid errors and to make calculations more efficient.