Question

What is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit?

13.4 units

17.9 units

26.8 units

40.0 units

Answer 1

see the attached figure to better understand the problem

Let

x------> the length side of a rectangle

y-------> the width side of a rectangle

we know that

the perimeter of a rectangle is equal to the formula

`P=2x+2y`

in this problem

`AB=DC=x`

`AD=BC=y`

Step 1

Find the distance AB

`A(-6,4)\\B(2,8)`

we know that

the distance's formula between two points is equal to

`d=\sqrt{(y2-y1)^(2) +(x2-x1)^(2)}`

substitute the values

`d=\sqrt{(8-4)^(2) +(2+6)^(2)}`

`d=\sqrt{(4)^(2) +(8)^(2)}`

`dAB=√(80)\ units`

Step 2

Find the distance BC

tex]B(2,8)\\C(4,4)[/tex]

we know that

the distance's formula between two points is equal to

`d=\sqrt{(y2-y1)^(2) +(x2-x1)^(2)}`

substitute the values

`d=\sqrt{(4-8)^(2) +(4-2)^(2)}`

`d=\sqrt{(-4)^(2) +(2)^(2)}`

`dBC=√(20)\ units`

Step 3

Find the perimeter

we know that

the perimeter of a rectangle is equal to the formula

`P=2x+2y`

`P=2AB+2BC`

we have

`dAB=√(80)\ units=8.9\ units`

`dBC=√(20)\ units=4.5\ units`

substitute the values of the distance in the formula

`P=2*8.9+2*4.5=26.8\ units`

therefore

the answer is

The perimeter of the rectangle is equal to
`26.8\ units`