Adding the distances between two consecutive vertices, the perimeter of JKLM is of [tex]10 + 6\sqrt{2}[/tex] units.
Given two points, [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex], the distance between them is of:
[tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Distance JK:
[tex]D = \sqrt{(3 - 0)^2 + (4 - 1)^2} = \sqrt{18} = 3\sqrt{2}[/tex]
Distance KL:
[tex]D = \sqrt{(8 - 3)^2 + (4 - 4)^2} = \sqrt{25} = 5[/tex]
Distance LM:
[tex]D = \sqrt{(5 - 8)^2 + (1 - 4)^2} = \sqrt{18} = 3\sqrt{2}[/tex]
Distance MJ:
[tex]D = \sqrt{(5 - 0)^2 + (1 - 1)^2} = \sqrt{25} = 5[/tex]
Thus, the perimeter, in units, is of:
[tex]P = 2(5 + 3\sqrt{2}) = 10 + 6\sqrt{2}[/tex]
A similar problem is given at https://brainly.com/question/20666716
