Given:
The perimeter of the rectangle, P=64 units.
From the figure, the length of the rectangle, l=PQ=3x+3.
The breadth of the rectangle, b=PS=2x-1.
Now, the expression for the perimeter of the rectangle can be written as,
[tex]\begin{gathered} P=2(l+b) \\ P=2(3x+3+2x-1) \\ P=2(5x+2) \\ P=2\times5x+2\times2 \\ P=10x+4 \end{gathered}[/tex]
Now, put P=64 in the above equation and solve for x.
[tex]\begin{gathered} 64=10x+4 \\ 64-4=10x \\ 60=10x \\ \frac{60}{10}=x \\ 6=x \end{gathered}[/tex]
Now, we know b=PS=2x-1.
Hence, PS can be calculated as,
[tex]\begin{gathered} PS=2x-1 \\ =2\times6-1 \\ =12-1 \\ =11 \end{gathered}[/tex]
Therefore, the length of side PS is 11 units.
