we know that
the perimeter of a rectangle is equal to
[tex]P=2x+2y[/tex]
where
x--------> is the length side of the room
y--------> is the width side of the room
In this problem we have
[tex]x=10\frac{9}{12}\ ft\\ \\y=8\frac{1}{2}\ ft[/tex]
Convert mixed number to an improper fractions
[tex]x=10\frac{9}{12}\ ft=\frac{10*12+9}{12}=\frac{129}{12}\ ft[/tex]
[tex]y=8\frac{1}{2}\ ft=\frac{8*2+1}{2}=\frac{17}{2}\ ft[/tex]
substitute the values in the formula of perimeter
[tex]P=2(\frac{129}{12})+2(\frac{17}{2})[/tex]
[tex]P=(\frac{129}{6})+17[/tex]
[tex]P=(21.5+17)\ ft[/tex]
[tex]P=38.5\ ft[/tex]
[tex]P=38 \frac{1}{2}\ ft[/tex]
therefore
the answer is
[tex]38 \frac{1}{2}\ ft[/tex]
