document.write( "Question 1084142: 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.
\n" ); document.write( "P.S. This is Geometry Summer work.. You don't have to help if you feel it is too hard or unnecessary. Thank you. \n" ); document.write( "

Algebra.Com's Answer #698205 by ikleyn(53765) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "1.  Mental solution\r\n" );
document.write( "\r\n" );
document.write( "    Let me make the length in 11  cm shorter (simply cutting off the rest of the rectangle).\r\n" );
document.write( "\r\n" );
document.write( "    Then I will get a square with the perimeter of 90 - 2*11 = 68 cm.\r\n" );
document.write( "\r\n" );
document.write( "    Then the side of the square is  = 17 cm.\r\n" );
document.write( "\r\n" );
document.write( "    Then the length of the original rectangle is 17 + 11 = 28 cm\r\n" );
document.write( "         The width of the original rectangle is 17 cm.\r\n" );
document.write( "\r\n" );
document.write( "    Check.  28 + 17 + 28 + 17 = 90 cm  Correct !\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "2.  Solution with one equation and one unknown\r\n" );
document.write( "\r\n" );
document.write( "     Let x be the length. Then the width is (x-11).\r\n" );
document.write( "\r\n" );
document.write( "     The perimeter is x + (x-11) + x + (x - 11) = 90,  or\r\n" );
document.write( "\r\n" );
document.write( "                      2x + 2x - 22 = 90,\r\n" );
document.write( "\r\n" );
document.write( "                      4x = 90 + 22 = 112,\r\n" );
document.write( "\r\n" );
document.write( "                      x =  = 28 cm.\r\n" );
document.write( "\r\n" );
document.write( "      Thus the length is 28 cm.  Then the width is 28 - 11 = 17 cm.\r\n" );
document.write( "\r\n" );
document.write( "      Same answer !!\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "3.   Two equations in two unknowns\r\n" );
document.write( "\r\n" );
document.write( "     2x + 2y = 90,   (1)\r\n" );
document.write( "      x -  y = 11.   (2)\r\n" );
document.write( "\r\n" );
document.write( "Simplify\r\n" );
document.write( "\r\n" );
document.write( "    x + y = 45,      (1')\r\n" );
document.write( "    x - y = 11.      (2')\r\n" );
document.write( "\r\n" );
document.write( "Add the two equations (1') and (2'). You will get\r\n" );
document.write( "\r\n" );
document.write( "    2x = 45 + 11 = 56  ====>  x =  = 28 cm for the length.\r\n" );
document.write( "\r\n" );
document.write( "    Etc.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "H a p p y l e a r n i n g ! !\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "--------------
\n" ); document.write( "For your summer Geometry classes, you have this free of charge online textbook on Geometry\r
\n" ); document.write( "\n" ); document.write( " GEOMETRY - YOUR ONLINE TEXTBOOK \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );