Given the figure, we can deduce the following information:
Perimeter = 65 in.
length = n
width = 11 2/4 in. = 23/2 in.
To determine the value of n, we use the formula:
[tex]P=2(l+w)[/tex]where:
P= Perimeter
l=length
w=width
We plug in what we know:
[tex]\begin{gathered} P=2(l+w) \\ 65=2(n+11\frac{2}{4}) \\ \text{Simplify and rearrange} \\ 65=2(n+\frac{23}{2}) \\ \frac{65}{2}=n+\frac{23}{2} \\ n=\frac{65}{2}-\frac{23}{2} \\ n=\frac{65-23}{2} \\ n=\frac{42}{2} \\ \text{Calculate} \\ n=21 \end{gathered}[/tex]Therefore, the value of n is 21 in.