Length of the rectangular patio = [tex]12\frac{1}{2}=\frac{25}{2}[/tex]
Let the width of the patio be = x
Area of the patio is given as = [tex]108\frac{1}{8}=\frac{865}{8}[/tex]
As the area of a rectangle is = length*width, so
[tex]\frac{865}{8}=(\frac{25}{2})x[/tex]
[tex]\frac{865}{8}*\frac{2}{25}=x[/tex]
x= [tex]\frac{1730}{200}[/tex] = [tex]\frac{173}{20}[/tex]
x = [tex]8\frac{13}{20}[/tex]
Hence, width of the patio is [tex]8\frac{13}{20}[/tex] feet.