Question

how would the perimeter be affected if the sides of the rectangles were increased a factor of k ?

Answer 1

Let we have a rectangle with the sides "x" and "y". The perimeter of this rectangle is x+x+y+y=2(x+y).
If we increase the sides "x" and "y" in k times (increase by factor of k) we obtain that the sides of the new rectangle is "kx" and "ky". So perimeter of the new rectangle is: 2kx+2ky=2k*(x+y).
Answer. Perimeter will increase by factor of k.