Respuesta :
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{5}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-5}) ~\hfill d1=\sqrt{[ 2- 5]^2 + [ -5- (-1)]^2} \\\\\\ d1=\sqrt{(-3)^2+(-5+1)^2}\implies d1=\sqrt{25}\implies \boxed{d1=5} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{-7}) ~\hfill d2=\sqrt{[ -3- 2]^2 + [ -7- (-5)]^2} \\\\\\ d2=\sqrt{(-5)^2+(-7+5)^2}\implies d2=\sqrt{25+4}\implies \boxed{d2=\sqrt{29}} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-1}) ~\hfill d3=\sqrt{[ 5- (-3)]^2 + [ -1- (-7)]^2} \\\\\\ d3=\sqrt{(5+3)^2+(-1+7)^2}\implies d3=\sqrt{100}\implies \boxed{d3=10} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{\large Perimeter}}{5+\sqrt{29}+10\implies 15+\sqrt{29}~~\approx~~20.39}[/tex]
