In the diagram, WZ =√26 . The perimeter of parallelogram WXYZ is + units

Solution:

The values of WXYZ given are

W(-2, 4), X (2, 4), Z (-3, -1) and Y(1, -1)

We have to find the perimeter of WXYZ

In order to find WZ let us make use of the distance formula for W(-2, 4) and Z(-3, -1)

Distance\(=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\)

Substituting the values

\(\\WZ=\sqrt{(-3-(-2))^{2}+((-1)-4)^{2}} \\ \\WZ=\sqrt{(-3+2)^{2}+(-1-4)^{2}} \\ \\WZ=\sqrt{(-1)^{2}+(-5)^{2}} \\ \\WZ=\sqrt{1+25} \\ \\WZ=\sqrt{26}\)

Where WZ is parallel to XY, so if WZ=√26 then XY = √26

WZ + XY = √26 + √26 = 2√26

Let us use the distance formula for W(-2, 4) and X(2, 4)

Distance\(=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\)

Substituting the values

WX\(=\sqrt{(2-(-2))^{2}+(4-4)^{2}} \\ \\WX=\sqrt{(2+2)^{2}+0} \\ \\WX=\sqrt{4^{2}} \\ \\WX=\sqrt{16}\)

WX = √16 = 4

It is parallel to the other side ZY = 4

WX + ZY = 4 + 4 = 8

Total perimeter = 8 + 2√26

Therefore, the perimeter is 8 + 2√26 units.

In the diagram, WZ =√26 . The perimeter of parallelogram WXYZ is + units

Summary:

In the diagram, WZ = √26. The perimeter of parallelogram WXYZ is 8 + 2√26 units.