Respuesta :

we must know the measure of each side, for this we must calculate the distance between points

the formula is

[tex]d=\sqrt[]{(x1-x2)^2+(y1-y2)^2}[/tex]

AB

[tex]\begin{gathered} \sqrt[]{(-6-(-3))^2+(2-6)^2} \\ \sqrt[]{25} \\ AB=5 \end{gathered}[/tex]

AC

[tex]\begin{gathered} \sqrt[]{(-6-5)^2+(2-0)^2} \\ \sqrt[]{125} \\ AC=5\sqrt[]{5} \end{gathered}[/tex]

BC

[tex]\begin{gathered} \sqrt[]{(-3-5)^2+(6-0)^2} \\ \\ \sqrt[]{100} \\ BC=10 \end{gathered}[/tex]

now add all sides to find the perimeter

[tex]\begin{gathered} 5+5\sqrt[]{5}+10 \\ \end{gathered}[/tex]

the perimeter is

[tex]15+5\sqrt[]{5}\approx26.18[/tex]