What is the perimeter of parallelogram WXYZ?
√5 +√17 units, 2√5+ 2√17 units, 16 units, 22 units

Solution:

From the figure,

W(0, -1), X(4, 0), Y(3, -2), Z(-1, -3)

We have to find the perimeter of the parallelogram WXYZ

Distance between the points can be found by using the formula

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

Now finding the distance between the given points,

\(\\WX =\sqrt{(4-0)^{2}+(0-(-1))^{2}}=\sqrt{(4)^{2}+(1)^{2}}\\WX=\sqrt{16+1}=\sqrt{17}\)

\(\\XY =\sqrt{(3-4)^{2}+(-2-0)^{2}}=\sqrt{(-1)^{2}+(-2)^{2}}\\XY=\sqrt{1+4}=\sqrt{5}\)

\(\\YZ =\sqrt{(-1-3)^{2}+(-3+2)^{2}}=\sqrt{(-4)^{2}+(-1)^{2}}\\YZ=\sqrt{16+1}=\sqrt{17}\)

\(\\ZX =\sqrt{(-1-0)^{2}+(-3+1)^{2}}=\sqrt{(-1)^{2}+(-2)^{2}}\\ZX=\sqrt{4+1}=\sqrt{5}\)

Now, perimeter of parallelogram = 2(WX + XY)

Perimeter = 2(√17 + √5) units

Therefore, the perimeter of the parallelogram is 2(√17 + √5) units.

What is the perimeter of parallelogram WXYZ?

Summary:

The perimeter of parallelogram WXYZ is 2(√17 + √5) units.