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.
