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