Algebra one binomial math story problems question

Question

 A projection  displays a  rectangular image on a wall. The height of the wall is X feet.  The area ( in square feet )  of the projection is represented by (x^2) - 12x +32.  The width of the projection is (X -4) feet.

       Write a binomial that represents the height of the projection.

Answer 1

x²-12x+32 = (x-4)(x-8)  by  factoring.  Since the projection's width is x-4, then the length must be x-8.

 

(It's OK if "width" > "length".