Answer :

5+5+7+7 is equal to 24 which is the perimeter

Answer:

[tex]P=24\ units[/tex]

Step-by-step explanation:

we know that

The perimeter of the rectangle is equal to

[tex]P=2L+2W[/tex]

where

L is the length side

W is the width side

In this problem we have

[tex]A(2,4),B(2,-1),C(-5,-1),D (-5,4)[/tex]    

using a graphing tool

Plot the points

see the attached figure to better understand the problem

[tex]L=BC[/tex]

[tex]W=AB[/tex]

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


[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]


Find the distance BC

[tex]B(2,-1),C(-5,-1)[/tex]

substitute

[tex]dBC=\sqrt{(-1+1)^{2}+(-5-2)^{2}}[/tex]    

[tex]dBC=\sqrt{49}=7\ units[/tex]    

Find the distance AB

[tex]A(2,4),B(2,-1)[/tex]

substitute

[tex]dAB=\sqrt{(-1-4)^{2}+(2-2)^{2}}[/tex]    

[tex]dAB=\sqrt{25}=5\ units[/tex]    

Find the perimeter

we have

[tex]L=dBC=7\ units[/tex]  

[tex]W=dAB=5\ units[/tex]    

substitute

[tex]P=2(7)+2(5)=24\ units[/tex]

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