Answer:
8 ft by 16 ft
Step-by-step explanation:
Let the width of the strip be x.
Then, the dimensions of the rug are (26-2x) and (18-2x).
So,
[tex](26-2x)(18-2x)=128 \\ \\ 4(13-x)(9-x)=128 \\ \\ (13-x)(9-x)=32 \\ \\ x^2 -22x+117=32 \\ \\ x^2 -22x+85 =0 \\ \\ (x-5)(x-17)=0 \\ \\ x=5, x=17[/tex]
If x=17, then both dimensions are less than 0, so x must equal 5.
So, the dimensions are 8 ft by 16 ft.