Question 1084142
.
<pre>
1.  <U>Mental solution</U>

    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 {{{68/4}}} = 17 cm.

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

    <U>Check</U>.  28 + 17 + 28 + 17 = 90 cm  Correct !



2.  <U>Solution with one equation and one unknown</U>

     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 = {{{112/4}}} = 28 cm.

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

      Same answer !!



3.   <U>Two equations in two unknowns</U>

     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 = {{{56/2}}} = 28 cm for the length.

    Etc.
</pre>

Solved.



H&nbsp;a&nbsp;p&nbsp;p&nbsp;y &nbsp;&nbsp;l&nbsp;e&nbsp;a&nbsp;r&nbsp;n&nbsp;i&nbsp;n&nbsp;g &nbsp;!&nbsp;!



--------------
For your summer Geometry classes, &nbsp;you have this free of charge online textbook on Geometry

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson>GEOMETRY - YOUR ONLINE TEXTBOOK</A> 

in this site.