ANSWER
PS = 13 units
Step-by-step explanation
The perimeter of the given rectangle is 46 units.
The perimeter of a rectangle is given as:
P = 2(L + B)
where L = length
B = breadth
From the figure:
L = 3z - 2
B = 2z
So, the perimeter is:
46 = 2(3z - 2 + 2z)
46 = 2(5z - 2)
Expand the bracket:
46 = 10z - 4
Collect like terms:
46 + 4 = 10z
50 = 10z
=> z = 50 / 10
z = 5
In a rectangle, opposite sides are equal. This means that:
PS = RQ = 3z - 2
PS = 3(5) - 2 = 15 - 2
PS = 13 units