Answer
length 12 feet, width 4 feet.
Work Step by Step
Step 1. Assume the width is $x$ feet; then the length is $2x+4$ feet.
Step 2. The area is given by $x(2x+4)=48$; we have $x^2+2x-24=0$ and $(x+6)(x-4)=0$
Step 3. Discard the negative solution; we have $x=4$ feet and $2(4)+4=12$ feet.
Step 4. The carpet's length is 12 feet and its width is 4 feet.
