Question

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

Answer 1

the perimeter of parallelogram wxyz is 1/2base×height
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Answer 2

The perimeter of parallelogram, WXYZ is 8+2$\sqrt{26}$.

WZ = 2$\sqrt{26}$.

Given

To find the perimeter of the parallelogram, WXYZ and value of WZ.

From the figure,      

It has four points WXYZ.      

Values of WXYZ are :  W(-2,4)    X(2,4)    Z(-3,-1)     Y(1,-1)

To find WZ :

Using distance formula for W(-2,4) and Z(-3,-1)

                   Distance = $\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2} }$

                   $x_1$ = -2         $x_2$ = -3      $y_1$ = 4      $y_2$ = -1

                             WZ = $\sqrt{(-3-(-2))^{2}+((-1)-(4))^{2} }$

                                    = $\sqrt{(-3+2)^{2}+(-1-4)^{2} }$    

                                    = $\sqrt{(-1)^{2}+(-5)^2 }$

                                    = $\sqrt{1+25}$

                             WZ = $\sqrt{26}$

Where, WZ is parallel to XY , so if WZ = $\sqrt{26}$ then, XY = $\sqrt{26}$.

Hence,    WZ + XY = $\sqrt{26}$ + $\sqrt{26}$ = 2$\sqrt{26}$.

Using distance formula for,  W(-2,4)    X(2,4)

                    Distance = $\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2} }$

                   $x_1$ = -2         $x_2$ = 2      $y_1$ = 4      $y_2$ = 4

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

So, WX = $\sqrt{16}$  = 4, which is parallel to the other side ZY = 4.

(i.e.,)   WX + ZY =  4 + 4 = 8.

Therefore, total perimeter of parallelogram WXYZ is 8 + 2$\sqrt{26}$.

To learn more...

1. brainly.in/question/1797838        

2. brainly.in/question/1427771