Start by calculating the length of each side by distance formula:
[tex]d = \sqrt{( ({y2 - y1})^{2}+ ( {x2 - x1})^{2}} )[/tex]
[tex]qr =\sqrt{(({y2 - y1})^{2}+({x2 - x1})^{2}} ) \\ \sqrt{( ({5 - 0})^{2} + ( {4 - 2})^{2}} ) \\ = \sqrt{{5}^{2} + {2}^{2}} = \sqrt{25 + 4} = \sqrt{29} [/tex]
[tex]rs =\sqrt{(({y2 - y1})^{2}+({x2 - x1})^{2}} ) \\ =\sqrt{(({7 - 5})^{2}+({8 - 4})^{2}} ) \\ = \sqrt{ {2}^{2} + {4}^{2}} = \sqrt{4 + 16} = \sqrt{20} \\ \sqrt{4} \: \times \sqrt{5} = 2 \sqrt{5} [/tex]
[tex]st =\sqrt{(({y2 - y1})^{2}+({x2 - x1})^{2}} ) \\=\sqrt{(({4 - 7})^{2}+({6 - 8})^{2}} ) \\=\sqrt{(({ - 3})^{2}+({ - 2})^{2}} ) = \sqrt{9 + 4} \\ = \sqrt{13} [/tex]
[tex]tu =\sqrt{(({y2 - y1})^{2}+({x2 - x1})^{2}} ) \\qr =\sqrt{(({3 - 4})^{2}+({10 - 6})^{2}} ) \\ \sqrt{( {( - 1)}^{2} + {(4)}^{2} )} = \sqrt{1 + 16} \\ = \sqrt{17} [/tex]
[tex]uq =\sqrt{(({y2 - y1})^{2}+({x2 - x1})^{2}} ) \\ =\sqrt{(({0 - 3})^{2}+({2 - 10})^{2}} ) \\ = \sqrt{ {( - 3)}^{2} + {( - 8)}^{2} } = \sqrt{9 + 64} \\ = \sqrt{73} [/tex]
Now we add up all 5 side lengths to find the perimeter: P = QR + RS + ST + TU + UQ
[tex]p = \sqrt{29} + 2 \sqrt{5} + \sqrt{13} + \sqrt{17} \\ + \sqrt{73} \\ = 5.39 + 4.47 + 3.61 + 4.12 \\ + \: 8.54 = 26.13 \: units[/tex]
Therefore B) 26.1 units is the closest answer
