Let's say we have a parallelogram that has sides of 2 and 3
perimeter = 2 * (side1 + side2)
perimeter = 2 * (2 + 3)
perimeter = 10
If the sides are increased by a factor 4, the sides are 8 and 12
perimeter = 2 * (side1 + side2)
perimeter = 2 * (8 + 12)
perimeter = 40
The perimeter increases by a factor 4.
