The perimeter of a rectangle is given by the formula:
[tex]P=2a+2b[/tex]Where a is the length of the vertical sides and b the length of the horizontal sides.
Now let's visualize the figure in the cartesian plane:
To find the length of the side b, we use the formula:
[tex]b=x2-x1[/tex]Where x2 and x1 are the x coordinates of the vertices of the bottom side.
To find the length of side a, we can use the formula:
[tex]a=y2-y1[/tex]Where y2 and y1 are the y-coordinates of the vertices of the left side.
In this case:
x2=5 and x1= -3
y2=9 and y1= -1
Then we get:
[tex]b=5-(-3)=5+3=8[/tex][tex]a=9-(-1)=9+1=10[/tex]Then the perimeter is:
[tex]P=2\times a+2\times b=2\times8+2\times10=36[/tex]Then, the perimeter of the rectangle equals 36
