The Solution.
Representing the problem in a diagram, we have
By formula,
[tex]P=2(L+W)[/tex]
In this case,
[tex]P=15\operatorname{cm},L=?,W=\frac{22}{8}cm[/tex]
Substituting these values in the formula above, we get
[tex]15=2(L+\frac{22}{8})[/tex]
Clearing the bracket, we get
[tex]15=2L+(2\times\frac{22}{8})[/tex][tex]\begin{gathered} 15=2L+\frac{11}{2} \\ \\ 15=2L+5.5 \end{gathered}[/tex][tex]\begin{gathered} 15-5.5=2L \\ 9.5=2L \end{gathered}[/tex]
Dividing both sides by 2, we get
[tex]L=\frac{9.5}{2}=4.75\approx4.8\operatorname{cm}[/tex]
Therefore, the correct answer is option C.
