Respuesta :
Perimeter of any figure is the sum of all sides
then to calculate sides of the triangle , we need the distance between each point, the distance between two points will be the length of a side
then to find the distance between two points we use the formula
[tex]d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}^{}[/tex](1,3) and (2,-3)
replacing
[tex]\begin{gathered} d_1=\sqrt[]{(1-2)^2+(3-(-3))^2} \\ d_1=\sqrt[]{(-1)^2+(6)^2} \\ d_1=\sqrt[]{1+36} \\ d_1=\sqrt[]{37}\approx6.08 \end{gathered}[/tex]first distance side is 6.08 units
(1,3) and (-1,-1)
replacing
[tex]\begin{gathered} d_2=\sqrt[]{(1-(-1))^2+(3-(-1))^2} \\ d_2=\sqrt[]{(2)^2+(4)^2} \\ d_2=\sqrt[]{4+16} \\ d_2=\sqrt[]{20}\approx4.47 \end{gathered}[/tex]second distance is 4.47 units
(2,-3) and (-1,-1)
replacing
[tex]\begin{gathered} d_3=\sqrt[]{(2-(-1))^2+(-3-(-1))^2} \\ d_3=\sqrt[]{(3)^2+(-2)^2} \\ d_3=\sqrt[]{9+4} \\ d_3=\sqrt[]{13}\approx3.6 \end{gathered}[/tex]Third distance is 3.6 units
Perimeter
sum all distances
[tex]\begin{gathered} P=\sqrt[]{37}+\sqrt[]{20}+\sqrt[]{13} \\ P\approx14.16 \end{gathered}[/tex]Perimeter of the triangle is 14.16 units
