We will have the following:
First, we are given the following expressions for the rectangle's length and width respectively:
[tex]l=w+6[/tex]&
[tex]w=w[/tex]Now, we calculate the length and width using the perimeter:
[tex]P=2(l+w)\Rightarrow P=2(w+6+w)\Rightarrow P=2(2w+6)\Rightarrow P=4(w+3)[/tex]So:
[tex]36=4(w+3)\Rightarrow w+3=9\Rightarrow w=6[/tex]Then:
[tex]l=(6)+6\Rightarrow l=12[/tex]So, the measurements of the length and the width are respectively 12 units and 6 units.
