1.  Mental solution

    Let me make the length in 11  cm shorter (simply cutting off the rest of the rectangle).

    Then I will get a square with the perimeter of 90 - 2*11 = 68 cm.

    Then the side of the square is  = 17 cm.

    Then the length of the original rectangle is 17 + 11 = 28 cm
         The width of the original rectangle is 17 cm.

    Check.  28 + 17 + 28 + 17 = 90 cm  Correct !



2.  Solution with one equation and one unknown

     Let x be the length. Then the width is (x-11).

     The perimeter is x + (x-11) + x + (x - 11) = 90,  or

                      2x + 2x - 22 = 90,

                      4x = 90 + 22 = 112,

                      x =  = 28 cm.

      Thus the length is 28 cm.  Then the width is 28 - 11 = 17 cm.

      Same answer !!



3.   Two equations in two unknowns

     2x + 2y = 90,   (1)
      x -  y = 11.   (2)

Simplify

    x + y = 45,      (1')
    x - y = 11.      (2')

Add the two equations (1') and (2'). You will get

    2x = 45 + 11 = 56  ====>  x =  = 28 cm for the length.

    Etc.