Opposite sides of a parallelogram,
[tex]\begin{gathered} QR=ST \\ 3y+8=y+22 \\ 3y-y=22-8 \\ 2y=14 \\ y=\frac{14}{2} \\ y=7 \end{gathered}[/tex]
Similarly, x can be obtained as,
[tex]\begin{gathered} RS=TQ \\ x-9=-3x+11 \\ x+3x=11+9 \\ 4x=20 \\ x=\frac{20}{4} \\ x=5 \end{gathered}[/tex][tex]\begin{gathered} Perimeter=(3y+8)+(x-9)+(y+22)+(-3x+11) \\ =\lbrack(3\times7)+8\rbrack+(5-9)+(7+22)+\lbrack(-3\times5)+11\rbrack \\ =\lbrack21+8\rbrack+(-4)+(29)+\lbrack-15+11\rbrack \\ =29-4+29-4 \\ =58-8 \\ =50 \end{gathered}[/tex]
Hence, the perimeter of the parallelogram is 50 units.
