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.