Given:
Area = 36 1/4 = 36.25 ft^2
Length = 8 3/4 = 8.75 ft
Unless this is a trick question, where the length can be found in the given values of the problem (where the answer would simply be L = 8.75ft), let us solve for the missing measurement, which is the width. A rug is rectangular, so to obtain the width, the area must be divided by the length. This is shown below:
Width = Area / Length
Width = 36.25 / 8.75
Width = 4.14 ft.
