We have a rectangular sheet with length (l) and width (w)
It is also given that length is four times the width,
[tex]\begin{gathered} l=4w \\ w=\frac{l}{4} \end{gathered}[/tex]The perimeter of the sheet must be less than 100 inches,
[tex]p<100\: [/tex]Recall that the perimeter of a rectangular shape is given by
[tex]p=2(l+w)[/tex]Substitute it into the above inequality
[tex]2(l+w)<100_{}[/tex]Now substitute the value of w into the above inequality.
[tex]2(l+\frac{l}{4})<100[/tex]Now let us simplify the above inequality
[tex]\begin{gathered} 2(l+\frac{l}{4})<100 \\ 2(\frac{4l+l}{4})<100 \\ 2(\frac{5l}{4})<100 \\ \frac{5l}{2}<100 \end{gathered}[/tex]Therefore, the possible lengths of the rectangular sheet are given by the inequality
[tex]\frac{5l}{2}<100[/tex]The 2nd option is the correct answer.
