Answer: second option, 2√5 + 2√(17)
Step-by-step explanation:
1) Perimeter = length of the four sides = length segment XY + length segment YZ + length segment ZW + length segment WX.
2) Condition of parallelograms: the opposite sides are parallel are have the same length.
Therefore,
- length segment XY = length segment ZW, and
- length segment YZ = length segment WX.
Hence, we just need to find the lengths of two segments, which you can do easily with the coordinate of the vertices shown in the diagram, and using Pythagora's theorem.
3) length segment XY = length segment ZW
(length segment XY)² = (4-3)² + (0 + 2)² = 1 + 4 = 5 ⇒
length segment XY = √5
4) length segment YZ = length segment WX
(length segment WX)² = (4-0)² + (0 + 1)² = 16 + 1 = 17 ⇒
length segment WX = √(17)
5) Perimeter = √5 + √5 + √(17) + √(17) = 2√5 + 2√(17), which is the second option.