Short Answer 
The length of side WX is 4 units and the length of side XY is ‚Äöao(26) units. The perimeter of parallelogram WXYZ is calculated as 8 + 2‚Äöao26 units.
Step 1: Calculate the Length of Side WX
To find the length of side WX, we use the distance formula between points. The formula is defined as:
- d = ‚ao((x2 Рx1)¬≤ + (y2 Рy1)¬≤)
By substituting the coordinates of points W (2, 4) and X (‚Äöai2, 4), we find:
- WX = ‚ao((‚ai2 Р2)¬≤ + (4 Р4)¬≤) = 4
Step 2: Calculate the Length of Side XY
Next, we apply the same distance formula to find the length of side XY. Using the coordinates of points X (‚Äöai2, 4) and Y (1, ‚Äöai1), we substitute them into the formula:
- XY = ‚ao((1 Р(‚ai2))¬≤ + (‚ai1 Р4)¬≤) = ‚ao(26)
This calculation yields XY = ‚Äöao(26), which represents the length of this side.
Step 3: Calculate the Perimeter of the Parallelogram
To find the perimeter P of parallelogram WXYZ, we sum the lengths of all sides. The formula for perimeter in a parallelogram is:
- P = 2(WX + XY)
Substituting the values we calculated, we find:
- P = 2(4) + 2(‚Äöao26) = 8 + 2‚Äöao26
Thus, the perimeter of parallelogram WXYZ is 8 + 2‚Äöao26 units.