The width of a rectangle is the length minus 6 units. The area of the rectangle is 27 units. What is the length, in units, of the rectangle?

9 units

Step-by-step explanation:

Area of rectangle= length ×width

Let the length of the rectangle be x units.

Width of rectangle= (x -6) units

Area of rectangle= 27 units²

x(x -6)= 27

x(x) -x(6)= 27          (expand bracket)

x² -6x -27= 0

(x -9)(x +3)= 0        (factorise)

x -9= 0  or  x +3= 0

x= 9       or       x= -3 (reject)

∴ The length of the rectangle is 9 units.

associative property of multiplication