Answer:
19 units
Step-by-step explanation:
Plot points A(5,2), B(-1,4), C(-2,1) and D(4,-1) on the coordinate plane. Find lengths of all sides as distances between two points:
[tex]AB=\sqrt{(-1-5)^2+(4-2)^2}=\sqrt{6^2+2^2}=\sqrt{36+4}=\sqrt{40}=2\sqrt{10}\ units\\ \\BC=\sqrt{(-2-(-1))^2+(1-4)^2}=\sqrt{1^2+3^2}=\sqrt{1+9}=\sqrt{10}\ units\\ \\CD=\sqrt{(4-(-2))^2+(-1-1)^2}=\sqrt{6^2+2^2}=\sqrt{36+4}=\sqrt{40}=2\sqrt{10}\ units\\ \\DA=\sqrt{(5-4)^2+(2-(-1))^2}=\sqrt{1^2+3^2}=\sqrt{1+9}=\sqrt{10}\ units[/tex]
The perimeter of the rectangle ABCD is
[tex]AB+BC+CD+DA=2\sqrt{10}+\sqrt{10}+2\sqrt{10}+\sqrt{10}=6\sqrt{10}\approx 18.97\ units\approx 19\ units[/tex]
