what is the perimeter of parallelogram wxyz?

5 square root symbol + 17 square root units
2 square root 5 + 2 square root 17 units
16 units
22 units

second option, 2√5 + 2√(17)

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,

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.