The width of a rectangle is 6 kilometers less than twice its length. if its area is 108 square kilometers, find the dimensions of the rectangle.

Let x = the length

2x - 6 = the width as given in the description.

Area of a rectangle is length * width. Now we plug in.

108 = x (2x - 6)

108 = 2x² - 6x

We are going to get all terms on the same side and factor.

2x² - 6x - 108 = 0

Factor out and divide each term by a GCF of 2 to get:

x² - 3x - 54 = 0

x² + 6x - 9x - 54 = 0

x (x + 6) - 9 (x + 6) = 0

Your factors are (x + 6) (x - 9) = 0. Now we set each binomial equal to zero. This gives us x = - 6 and x = 9. Distance cannot be measure in negative numbers so we know to use x = 9 to find our measurements.

The length (x) is 9 kilometers. The width (2x - 6) is 12 kilometers when you plug in 9 where the x is.