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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]
