see the attached figure to better understand the problem
Let
x------> the length side of a rectangle
y-------> the width side of a rectangle
we know that
the perimeter of a rectangle is equal to the formula
[tex]P=2x+2y[/tex]
In this problem
[tex]AB=DC=x\\AD=BC=y[/tex]
Step 1
Find the distance AB
[tex]A(-6,4)\\B(4,2)[/tex]
we know that
the distance's formula between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}[/tex]
substitute the values
[tex]dAB=\sqrt{(2-4)^{2} +(4+6)^{2}}[/tex]
[tex]dAB=\sqrt{(-2)^{2} +(10)^{2}}[/tex]
[tex]dAB=\sqrt{104}\ units=10.2\ units[/tex]
Step 2
Find the distance BC
[tex]B(4,2)\\C(3,-3)[/tex]
we know that
the distance's formula between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}[/tex]
substitute the values
[tex]dBC=\sqrt{(-3-2)^{2} +(3-4)^{2}}[/tex]
[tex]dBC=\sqrt{(-5)^{2} +(-1)^{2}}[/tex]
[tex]dBC=\sqrt{26}\ units=5.1\ units[/tex]
Step 3
Find the perimeter
we know that
the perimeter of a rectangle is equal to the formula
[tex]P=2x+2y[/tex]
[tex]P=2AB+2BC[/tex]
substitute the values of the distance in the formula
[tex]P=2*10.2+2*5.1=30.6\ units[/tex]
therefore
the answer is
The perimeter of the rectangle is equal to [tex]30.6\ units[/tex]
