Answer: The answer is (C) 44 units.
Step-by-step explanation: ABCD is a parallelogram in the given figure, where the lengths of the sides are
AB = 4y - 2, BC = 2x + 2, CD = 2y + 6 and DA = 3x - 1.
We know that the opposite sides of a parallelogram are equal, so we ahve
AB = CD and BC = DA.
Therefore, we have
[tex]4y-2=2y+6\\\\\Rightarrow 4y-2y=6+2\\\\\Rightarrow 2y=8\\\\\Rightarrow y=4,[/tex]
and
[tex]2x+2=3x-1\\\\\Rightarrow 3x-2x=2+1\\\\\Rightarrow x=3.[/tex]
So, x = 3 and y = 4.
Hence, the perimeter will be
[tex]p=AB+BC+CD+DA=4y-2+2x+2+2y+6+3x-1=5x+6y+5\\\\\Rightarrow p=5\times 3+6\times 4+5=15+24+5=44.[/tex]
Thus, the correct option is (C) 44 units.
