Find an expression in simplified form for the perimeter of Sally's patio?

Question

Sally's rectangular patio has a length of (5x - 2) meters and an area (A) of 15x² - 11x + 2 square meters

 

find an expression in simplified form for the perimeter of Sally's patio

Answer 1

given:     length of (5x - 2) meters 

 

formulas:     area = (length)*(width)

                (perimeter) = 2*(length) + 2*(width)

 

So, what is the width?

          (width) = (area) / (length)

 

       (width) = (15x² - 11x + 2) / (5x-2)

                   = (3x-1)*(5x - 2) / (5x - 2)                 [factor the numerator]

                   = (3x+1)                                             [cancel]

 

     (perimeter) = 2*(length) + 2*(width)

                   = 2*(5x-2) + 2*(3x+1)

                   = 10x - 4  +  6x + 2

      (perimeter) = (16x - 2)  square meters                    [simplified]