we know that
In a Rhombus all sides are congruent
so
AB=BC=CD=AD
Find the distance AB
[tex] A( 1,1)\\B(-2,-3)[/tex]
The distance formula between two points is equal to
[tex] d=\sqrt{(y2-y1)^{2} + (x2-x1)^{2}} [/tex]
[tex] d=\sqrt{(-3-1)^{2} + (-2-1)^{2}} [/tex]
[tex] d=\sqrt{(-4)^{2} + (-3)^{2}} [/tex]
[tex]d=\sqrt{25}=5\ units[/tex]
Find the perimeter of a Rhombus
the perimeter of a rhombus is equal to
[tex] P=4d [/tex]
where d is the length side of the rhombus
in this problem
[tex] d=5\ units[/tex]
so
[tex] P=4*5 [/tex]
[tex] P=20\ units[/tex]
therefore
the answer is
The perimeter of the rhombus is equal to [tex] 20\ units[/tex]
