Answer :

The perimeter of the given rectangle is, 19.2112

Given that, the vertices of the rectangle are A(-3,-2), B(-5,-5), C(1,-5), D(3,-2) .

to find the perimeter through the given vertices, we need to calculate the distance from the vertices AB,BC,CD,DA.

we already know that the sum of all sides of the rectangle is known as the perimeter of the rectangle.

Using distance formula between 2 vertices , √[(x2-x1)²+(y2-y1)²]

AB = √[(-5+3)²+(-5+2)²]

     = √[(-2)²+(-3)²]

     =  √[4+9]

     =  √[13]

     =  √13

AB = 3.6056

BC = √[(1+5)²+(-5+5)²]

     = √[(6)²+(0)²]

     =  √[36+0]

     =  √[36]

     =  √36

BC = 6

CD = √[(3-1)²+(-2+5)²]

     = √[(2)²+(3)²]

     =  √[4+9]

     =  √[13]

     =  √13

CD = 3.6056

DA = √[(-3-3)²+(-2+2)²]

     = √[(-6)²+(0)²]

     =  √[36+0]

     =  √[36]

     =  √36

DA = 6

Therefore perimeter of the rectangle with given vertices is ,

  = AB+BC+CD+DA

  = 3.6056+6+3.6056+6

  = 19.2112

  = 19 (rounded to nearest tenth).

Therefore the perimeter of the rectangle with given vertices is 19.2112

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