PUMaC 2020 Team Problem 5

Suppose two polygons may be glued together at an edge if and only if corresponding edges of the same length are made to coincide. A 3 \times 4 rectangle is cut into n pieces by making straight line cuts. What is the minimum value of n so that it’s possible to cut the pieces in such a way that they may be glued together two at a time into a polygon with perimeter at least 2021?