The perimeter of the parallelogram is [tex]2\sqrt{85}+12[/tex]
Explanation
According to the diagram below, Vertices of the parallelogram ABCD are: A (-3, 1) , B (4, 7) , C (4, 1) and D (-3, -5)
Using distance formula.....
Length of AB [tex]= \sqrt{(-3-4)^2+(1-7)^2}=\sqrt{(-7)^2+(-6)^2}= \sqrt{49+36}=\sqrt{85}[/tex]
Length of BC [tex]=\sqrt{(4-4)^2+(7-1)^2}=\sqrt{0+6^2}=\sqrt{36}=6[/tex]
As the opposite sides are equal in any parallelogram, so [tex]CD=AB=\sqrt{85}[/tex] and [tex]AD=BC= 6[/tex]
Thus the perimeter [tex]=2(\sqrt{85} +6)= 2\sqrt{85}+12[/tex]
