SOLUTION: The length of a rectangle is 11 centimeters more than its width. The perimeter is 90 centimeters. Find the length and width of the rectangle. P.S. This is Geometry Summer work..

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.