Since the figure is a parallelogram, then SP=RQ, and SR=PQ.
To find SR, we draw right triangle SAR, as shown in the picture, where the coordinates of A are clearly (-3, -2).
Thus, we can see that SA=4 units, and AR=4 units. By the Pythagorean theorem,
[tex]SR= \sqrt{4^2+4^2}= \sqrt{2\cdot4^2}=4 \sqrt{2}. [/tex]
Similarly, to find SP, which is equal to QR, we draw the triangle PBS, where the coordinates of B are (-2, 2).
Clearly, PB=3 and SB=1, thus using the Pythagorean theorem in right triangle PBS:
[tex] SP= \sqrt{1^2+3^2}= \sqrt{10} [/tex] units.
The perimeter of the parallelogram is SP+RQ+SR+PQ=
[tex]\sqrt{10} +\sqrt{10} +4 \sqrt{2}+4 \sqrt{2}=2\sqrt{10} +8 \sqrt{2}[/tex].
Answer: second choice
