Answer:
21.6
Step-by-step explanation:
To find the perimeter of rectangle WXYZ with vertices W(-3,7) X(-5,4) , Y(1,0) and Z(3,3), we first need to find the length WX, XY, YZ and WZ.
We know the distance formula between the coordinates [tex]\left ( x_{1},y_{1} \right ) \text{and} \left ( x_{2},y_{2} \right )[/tex] is [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
[tex]WX=\sqrt{(-5+3)^{2} +(4-7)^{2} } =\sqrt{4+9}=\sqrt{74}=3.60[/tex]
[tex]XY=\sqrt{(1+5)^{2} +(0-4)^{2} } =\sqrt{36+16}=\sqrt{52}=7.21[/tex]
[tex]YZ=\sqrt{(3-1)^{2} +(3-0)^{2} } =\sqrt{4+9}=\sqrt{13}=3.60[/tex]
[tex]WZ=\sqrt{(3+3)^{2} +(3-7)^{2} } =\sqrt{36+16}=\sqrt{52}=7.21[/tex]
Now, rounding each side to the nearest tenth we have,
[tex]WX=3.6[/tex]
[tex]XY=7.2[/tex]
[tex]YZ=3.6[/tex]
[tex]WZ=7.2[/tex]
Now, perimeter of rectangle WXYZ[tex]=2(WX+WZ)[/tex]
[tex]=2(3.6+7.2)[/tex]
[tex]=2(10.8)[/tex]
[tex]=21.6[/tex]
Hence, perimeter of rectangle WXYZ is 21.6.
