In order to find the Perimeter of the Rectangle, First we need to find the Length and Width of the Rectangle.
Distance between two points (x₁ , y₁) and (x₂ , y₂) is given by :

There are two lengths in a rectangle. Let us find any one length of the rectangle.
I'm considering the length with co-ordinates (-8 , 2) and (-2 , 10)
Here : x₁ = -8 and x₂ = -2 and y₁ = 2 and y₂ = 10
Substituting the values in the distance formula, We get :
![\mathsf{\implies Length = \sqrt{[-2 - (-8)]^2 + [10 - 2]^2}}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cimplies%20Length%20%3D%20%5Csqrt%7B%5B-2%20-%20%28-8%29%5D%5E2%20%2B%20%5B10%20-%202%5D%5E2%7D%7D)
![\mathsf{\implies Length = \sqrt{[-2 + 8]^2 + [8]^2}}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cimplies%20Length%20%3D%20%5Csqrt%7B%5B-2%20%2B%208%5D%5E2%20%2B%20%5B8%5D%5E2%7D%7D)
![\mathsf{\implies Length = \sqrt{[6]^2 + [8]^2}}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cimplies%20Length%20%3D%20%5Csqrt%7B%5B6%5D%5E2%20%2B%20%5B8%5D%5E2%7D%7D)



There are two widths in a rectangle. Let us find any one width of the rectangle.
I'm considering the width with co-ordinates (-2 , 10) and (2 , 7)
Here : x₁ = -2 and x₂ = 2 and y₁ = 10 and y₂ = 7
Substituting the values in the distance formula, We get :
![\mathsf{\implies Width = \sqrt{[2 - (-2)]^2 + [7 - 10]^2}}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cimplies%20Width%20%3D%20%5Csqrt%7B%5B2%20-%20%28-2%29%5D%5E2%20%2B%20%5B7%20-%2010%5D%5E2%7D%7D)
![\mathsf{\implies Width = \sqrt{[2 + 2]^2 + [-3]^2}}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cimplies%20Width%20%3D%20%5Csqrt%7B%5B2%20%2B%202%5D%5E2%20%2B%20%5B-3%5D%5E2%7D%7D)
![\mathsf{\implies Width = \sqrt{[4]^2 + [-3]^2}}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cimplies%20Width%20%3D%20%5Csqrt%7B%5B4%5D%5E2%20%2B%20%5B-3%5D%5E2%7D%7D)



Perimeter of a Rectangle is given by : 2[Length + Width]
Perimeter of the given rectangle = 2[10 + 5]
Perimeter of the given rectangle = 2[15]
Perimeter of the given rectangle = 30
<u>Answer</u> : Perimeter of the given rectangle is 30 square units