In the diagram, the length of PS is 18.5 units
How to find the length of PS
The length of PS is solved using the proportions as follows
RS / PS = QR / QP
From the figure, we have the values substituted as
(2x + 3) / (3x - 1) = 32 / 40
cross multiply
40 (2x + 3) = 32 (3x - 1)
80x + 120 = 96x - 32
120 + 32 = 96x - 80x
152 = 16x
x = 152 / 16
x = 9.5
The length of PS = 3x - 1
= 3 * 9.5 - 1
= 18.5 units