Answer:
Perimeter of rectangle ABCD = 9.64 units
Step-by-step explanation:
The formula used to calculate perimeter of rectangle is:
[tex]Perimeter\: of\: rectangle=2(Length+ Width)[/tex]
We know that rectangle has opposite sides same i.e Length (AB and CD) are same and Width( AD and BD) are same
We need to find Length and Width to find the perimeter
So, if we find Length AB and Width AC we can find perimeter
Finding Length AB
The length AB can be found using distance formula: [tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have A =(-6,-4) and B(-4,-4)
So, x_1=-6, y_1=-4, x_2=-4, y_2=-4
Putting values in formula and finding length
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(-4-(-6))^2+(-4-(-4))^2}\\Distance=\sqrt{(-4+6)^2+(-4+4)^2}\\Distance=\sqrt{(2)^2+(0)^2}\\Distance=\sqrt{4+0}\\Distance = 2[/tex]
So, Length AB = 2
Now, Finding Width AC
The length AB can be found using distance formula: [tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have A =(-6,-4) and C(-4,-2)
So, x_1=-6, y_1=-4, x_2=-4, y_2=-2
Putting values in formula and finding length
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(-6-(-4))^2+(-4-(-2))^2}\\Distance=\sqrt{(-6+4)^2+(-4+2)^2}\\Distance=\sqrt{(-2)^2+(-2)^2}\\Distance=\sqrt{4+4}\\Distance = \sqrt{8}\\Distance=2.82[/tex]
So, Width AD = 2.82
Now, We have Length = 2 and Width = 2.82
Finding perimeter of rectangle
[tex]Perimeter\: of\: rectangle=2(Length+ Width)\\Perimeter\: of\: rectangle=2(2+ 2.82)\\Perimeter\: of\: rectangle=2(4.82)\\Perimeter\: of\: rectangle=9.64[/tex]
So, Perimeter of rectangle ABCD = 9.64 units
