How do I calculate the length of a regular pentagon's edge when I know that it has the same perimeter as a triangle who's perimeter is 30cm?

The first thing I would do is sketch a diagram of a triangle and a pentagon. I find that tutees learn best when they can see what's going on so this makes the explanation easier to understand. After having sketched the triangle and pentagon, I would label the side of the pentagon as x. After that, we can find the side of the triangle since we know that in a regular triangle all 3 sides are the same. 30/3 = 10. We know that the perimeter of a pentagon is also 30 and with a regular pentagon all 5 sides have the same length therefore 30/5 gives us 6 which is our answer. After having done this, we can see that it was not necessary to find the sides of the triangle. I would explain this to my tutee and let them know that skipping this step would allow them to save time under test conditions.