Since a rectangular patio is a rectangle, to solve this we are going to use the formula for the area of a rectangle: \(A=wl\)
where
\(A\) is the area of the rectangle
\(w\) is the width of the rectangle
\(l\) is the length of the rectangle
We know form our problem that the length of the rectangular patio is \(12\frac{1}{2}\) feet, so \(l=12\frac{1}{2} ft\). We also know that the area is \(103\frac{1}{8}\) square feet, so \(A=103\frac{1}{8} ft^2\). Lets replace those values in our formula and solve for \(w\):
\(A=wl\)
\(103\frac{1}{8} ft^2=12\frac{1}{2}ftw\)
\(\frac{103\frac{1}{8}ft^2}{12\frac{1}{2}ft} =w\)
\(w=\frac{103\frac{1}{8}ft^2}{12\frac{1}{2}ft}\)
\(w=8\frac{1}{4} ft=8.25ft\)
We can conclude that the width of the rectangular patio is \(8\frac{1}{4}\) feet, or as a decimal, 8.25 feet.
