What is the perimeter in square units of the rectangle shown on the coordinate grid?

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 :

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 :

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

Answer : Perimeter of the given rectangle is 30 square units

A

Step-by-step explanation:

The opposite sides of a rectangle are congruent.

Calculate the lengths of 2 of the sides using the distance formula and multiply by 2

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 2, 10) and (x₂, y₂ ) = (2, 7)

d =

   =

   = = = 5

Repeat

with (x₁, y₁ ) = (- 8, 2) and (x₂, y₂ ) = (- 2, 10)

d =

  =

   = = = 10

Hence

Perimeter = (2 × 5) + (2 × 10) = 10 + 20 = 30 units → A

step-by-step explanation:

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