The lower value of the perimeter is 140 inches .
Width of the rectangle is 20 inches .
The length of the rectangle is calculated as ,
[tex]\begin{gathered} \text{Perimeter = 2 ( Length + width )} \\ 140=\text{ 2 ( Length + }20\text{ )} \end{gathered}[/tex]Rearranging the terms ,
[tex]\begin{gathered} \text{Length + 20 = }\frac{140}{2} \\ \text{Length + 20 = 70} \\ \text{Length = 50 inches} \end{gathered}[/tex]The higher value of perimeter is 220 inches .
Width of the rectangle is 20 inches .
The length is calculated as,
[tex]\begin{gathered} \text{Perimeter = 2 ( Length + width )} \\ 220=\text{ 2 ( Length + }20\text{ )} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \text{Length + 20 = 110} \\ \text{Length = 110 - 20} \\ \text{Length = 90 inches} \end{gathered}[/tex]Thus the range of values for the length of the given rectangle are 50 and 90 .
