Answer
The border has a width of 1ft.
Work Step by Step
X represents the amount of extra space after the carpet is laid down on all sides.
$$24=10x+2x(9-2x)$$
$$24=10x+18x-4x^2$$
$$4x^2-28x+24=0$$
$$x^2-7x+6=0$$
$$(x-1)(x-6)=0$$
$$x=1,6$$
6 ft is not a possible solution.
$$x=1$$
The border has a width of 1ft.
