The yard behind the cindy's house is rectangular in shape and has a perimeter of 72 feet. if the length l of the yard is 18 feet longer than the width w of the yard, what is the area of the yard, in square feet?

Let the width of the yard  be w.
Since the length is 18feet longer, l = w + 18

Perimeter for rectangle =  2(l + w)

        2(l + w) = 72
      
        2(w+18 + w) = 72      Divide 2 on both sides

           (w + 18 + w) = 36

               2w + 18 =   36

                       2w = 36 - 18

                            2w = 18       Divide 2 on both sides

                                w = 18/2

                                   w = 9

Recall, length l = w + 18, l = 9 + 18 = 27

Hence width, w = 9, length,l = 27

Area of rectangle = l × w = 27 × 9 =   243

Area of rectangular yard =  243 square feet.