The perimeter of a standard-sized reclangular rug is 32 ft . The length is 2 ft longer than the width. Find the dimensions. The width is \( \square \mathrm{ft} \). The length is \( \square \mathrm{ft} \).

To find the dimensions of the rug, we can start by defining the width as \( w \) ft. Given that the length is 2 ft longer than the width, we can express the length as \( w + 2 \) ft. The formula for the perimeter \( P \) of a rectangle is given by: \[ P = 2(\text{length} + \text{width}) \] Substituting the known values, we have: \[ 32 = 2((w + 2) + w) \] Simplifying this equation: \[ 32 = 2(2w + 2) \] \[ 32 = 4w + 4 \] \[ 32 - 4 = 4w \] \[ 28 = 4w \] \[ w = 7 \text{ ft} \] Now, calculating the length: \[ \text{length} = w + 2 = 7 + 2 = 9 \text{ ft} \] Thus, the width is \( 7 \) ft and the length is \( 9 \) ft. The width is \( 7 \mathrm{ft} \). The length is \( 9 \mathrm{ft} \).