The perimeter of a rectangle is 48 m. if the width were doubled and the length were increased by 24 m, the perimeter would be 112 m. what is the length of the original rectangle?

Original

Length (L): L

width (w): w

Perimeter (P) = 2L + 2w

               48 = 2(L) + 2(w)

              24 = L + w    

         24 - L = w

New

Length (L): L + 24

width (w): 2w        ⇒2(24 - L)   = 48 - 2L

Perimeter (P) = 2L + 2w

               112 = 2(L + 24) + 2(48 - 2L)

                112 = 2L + 48 + 96 - 4L

                 112 = -2L + 140

                 -28 = -2L

                   14 = L

14 m