Answer:
[tex]P=33.9\ units[/tex]
Step-by-step explanation:
we know that
The perimeter of a rectangle is equal to
[tex]P=2(L+W)[/tex]
where
L is the length of rectangle
W is the width of rectangle
Let
[tex]A(-3,-4),B(-6,-1),C(3,8),D(6,5)[/tex]
Remember that
[tex]W=AB=CD\\L=BC=AD[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
step 1
Find the distance AB
[tex]A(-3,-4),B(-6,-1)[/tex]
substitute in the formula
[tex]d=\sqrt{(-1+4)^{2}+(-6+3)^{2}}[/tex]
[tex]d=\sqrt{(3)^{2}+(-3)^{2}}[/tex]
[tex]d_A_B=\sqrt{18}=4.24\ units[/tex]
step 2
Find the distance BC
[tex]B(-6,-1),C(3,8)[/tex]
substitute in the formula
[tex]d=\sqrt{(8+1)^{2}+(3+6)^{2}}[/tex]
[tex]d=\sqrt{(9)^{2}+(9)^{2}}[/tex]
[tex]d_B_C=\sqrt{162}=12.73\ units[/tex]
step 3
Find the perimeter
[tex]P=2(12.73+4.24)[/tex]
[tex]P=33.94\ units[/tex]
Round to the nearest tenth
[tex]P=33.9\ units[/tex]
