To solve this problem, we will use the following formula for the distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.[/tex]
The distance between (-8,-2) and (1,10) is:
[tex]d_1=\sqrt{(-8-1)^2+(-2-10)^2}=\sqrt{81+144}=\sqrt{225}=15.[/tex]
The distance between (1,10) and (17,-2) is:
[tex]d_2=\sqrt{(1-17)^2+(10-(-2))^2}=\sqrt{256+144}=\sqrt{400}=20.[/tex]
The distance between (-8,-2) and (17,-2) is:
[tex]d_3=\sqrt{(-8-17)^2+(-2-(-2))^2}=\sqrt{25^2}=25.[/tex]
Therefore, the perimeter of the triangle is:
[tex]P=15+20+25=60.[/tex]
Answer:
[tex]60.[/tex]
