Answer:
[tex]2\sqrt{5}+\sqrt{29}+\sqrt{53},\\\approx 17.14\:\mathrm{units}[/tex]
Step-by-step explanation:
The distance between two coordinates is given by:
[tex]d=\sqrt{(\Delta x)^2+(\Delta y)^2}[/tex], or [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex].
The distance between each of the coordinates of the triangle forms the sides of triangle. Therefore, we can add the distance between these coordinates to find the perimeter of the triangle.
The distance between [tex](3, -2)[/tex] and [tex](7, 0)[/tex] is:
[tex]d=\sqrt{(7-3)^2+(0-(-2))^2}=\sqrt{4^2+2^2}=\sqrt{20}=2\sqrt{5}[/tex]
The distance between [tex](3, -2)[/tex] and [tex](5, 5)[/tex] is:
[tex]d=\sqrt{(5-3)^2+(5-(-2))^2}=\sqrt{2^2+7^2}=\sqrt{53}}[/tex]
[tex]d=\sqrt{(7-5)^2+(0-5)^2}=\sqrt{2^2+5^2}=\sqrt{29}[/tex].
Therefore, the total perimeter of the triangle is:
[tex]\fbox{$2\sqrt{5}+\sqrt{29}+\sqrt{53}\:\checkmark$}[/tex].
