Question

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

12.7 units

16.9 units

24.0 units

33.9 units

Answer 1

33.9

Explanation:

Answer 2

`P=33.9\ units`

Explanation:

we know that

The perimeter of a rectangle is equal to

`P=2(L+W)`

where

L is the length of rectangle

W is the width of rectangle

Let

`A(-3,-4),B(-6,-1),C(3,8),D(6,5)`

Remember that

`W=AB=CD\\L=BC=AD`

the formula to calculate the distance between two points is equal to

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

step 1

Find the distance AB

`A(-3,-4),B(-6,-1)`

substitute in the formula

`d=\sqrt{(-1+4)^(2)+(-6+3)^(2)}`

`d=\sqrt{(3)^(2)+(-3)^(2)}`

`d_A_B=√(18)=4.24\ units`

step 2

Find the distance BC

`B(-6,-1),C(3,8)`

substitute in the formula

`d=\sqrt{(8+1)^(2)+(3+6)^(2)}`

`d=\sqrt{(9)^(2)+(9)^(2)}`

`d_B_C=√(162)=12.73\ units`

step 3

Find the perimeter

`P=2(12.73+4.24)`

`P=33.94\ units`

Round to the nearest tenth

`P=33.9\ units`