Answer:
The strip would be 2 ft wide
Step-by-step explanation:
Let the strip be x ft long
since it is on either sides, it will take a space each of 2x
So the dimensions of the rug will be;
(8-2x) and (12-2x)
The product of these will give the area of the rug
We have this as;
(8-2x)(12-2x) = 32
96-16x-24x + 4x^2 = 32
4x^2-40x + 96-32 = 0
4x^2 -40x + 64 = 0
x^2 - 10x + 16 = 0
x^2 - 8x - 2x + 16 = 0
x(x-8) -2(x-8) = 0
(x-2)(x-8) = 0
x = 2 or 8
The value 8 will not be possible as it will need to negative dimensions
So the possible dimensions will be;
(8-2(2)) and 12-2(2)
= 8-4 and 12-4
= 4 ft by 8 ft
