Catarina and Tom want to buy a rug for a room that is 8 by 12. They want to leave an even strip of flooring uncovered around the edges of the room. How wide a stip willhave if they buy a rug with an area of 32 square feet

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