The perimeter of the given rectangle is 78 units.
Recall that the perimeter of a rectangle is given by

Where w is the width and l is the length of the rectangle.
As you can see from the given figure,
w = 3z + 3
l = 4z + 1
We are asked to find the side length of side PS.
Substitute the given values into the above formula and solve for z.

So, the value of z is 5
Finally, the length of side PS is

Therefore, the length of the side PS is 21 units.