Answer:
\(P=24\ units\)
Step-by-step explanation:
we know that
The perimeter of the rectangle is equal to
\(P=2L+2W\)
where
L is the length side
W is the width side
In this problem we have
\(A(2,4),B(2,-1),C(-5,-1),D (-5,4)\)
using a graphing tool
Plot the points
see the attached figure to better understand the problem
\(L=BC\)
\(W=AB\)
the formula to calculate the distance between two points is equal to
\(d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}\)
Find the distance BC
\(B(2,-1),C(-5,-1)\)
substitute
\(dBC=\sqrt{(-1+1)^{2}+(-5-2)^{2}}\)
\(dBC=\sqrt{49}=7\ units\)
Find the distance AB
\(A(2,4),B(2,-1)\)
substitute
\(dAB=\sqrt{(-1-4)^{2}+(2-2)^{2}}\)
\(dAB=\sqrt{25}=5\ units\)
Find the perimeter
we have
\(L=dBC=7\ units\)
\(W=dAB=5\ units\)
substitute
\(P=2(7)+2(5)=24\ units\)
