The room is a rectangle. This means it has opposite sides with the same measure. So, two of the sides measure 14 ft 9 in, and the two other sides measure 13 ft.
Thus, the perimeter is the sum of the measures of all four sides:
[tex]2\cdot(14\text{ft}+9\text{in})+2\cdot(13\text{ft})=28\text{ft}+18\text{in}+26\text{ft}=54\text{ft}+18\text{in}[/tex]Now, notice that we can also convert 18in to ft:
[tex]\begin{gathered} 18\text{in}=1.5\text{ft} \\ \\ \Rightarrow54\text{ft}+18\text{in}=(54+1.5)\text{ft}=55.5\text{ft} \end{gathered}[/tex]So, the perimeter of the dining room is 55.5 feet.