The length of a rectangle is 2 feet less than twice the width. The area of the rectangle is 180 feet squared. Find the length and width of the rectangle.

Let the width of rectangle be x

then, length of rectangle will be 2x - 2

Area of rectangle = 180 

Formula : Area of rectangle = length * Width

                                         180  = (x) * (2x-2) 

                                          180 = 2x^2 - 2x

transposing 180 to the other side, we get 

                                        2x^2 - 2x -180 =0

dividing 2 from both sides, we get

                                      2x^2/2 - 2x/2 -180/2 =0/2

                                                x^2 -x -90=0

Now, by using middle term split method:

                                         x^2 - 10x +9x -90 =0 

                                        x(x -10) + 9 (x-10) =0 

                                         (x+9) (x-10) =0

let, x + 9= 0

     x = -9  ( it is not possible because width cannot be in negative)

Let, x-10 =0 

             x = 10

So, Width = 10 feet

and, Length = 2(10) - 2

                     = 20 - 2

                    = 18 feet 

Thus, Length and Width of a rectangle are 18 feet and 10 feet respectively.