Answer:
[tex]9\sqrt{2}+\sqrt{82}[/tex]
Step-by-step explanation:
The distance between the points (x1,y1) and (x2,y2) is given by:
[tex]d=\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
By using the above formula we can find the length of sides of the triangle
Distance between (2,2) and (6,6):
[tex]d=\sqrt{(6-2)^2+(6-2)^2}[/tex]
[tex]d=\sqrt{4^2+4^2}\\ \\d=\sqrt{2\times 4^2}\\ \\d=4\sqrt{2}[/tex]
Distance between (2,2) and (7,-3):
[tex]d=\sqrt{(7-2)^2+(-3-2)^2}[/tex]
[tex]d=\sqrt{5^2+5^2}\\ \\d=5\sqrt{2}[/tex]
and Distance between (6,6) and (7,-3):
[tex]d=\sqrt{(7-6)^2+(-3-6)^2}[/tex]
[tex]d=\sqrt{1^2+9^2}\\ \\d=\sqrt{82}[/tex]
Hence, perimeter of triangle=sum of length of all three sides
= [tex]4\sqrt{2} +5\sqrt{2} +\sqrt{82}[/tex]
= [tex]9\sqrt{2}+\sqrt{82}[/tex]
