document.write( "Question 1169901: If the perimeter of a rectangle is 44 cm and the area is 105 square cm, then what are the dimensions of the rectangle?
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #794750 by ikleyn(52788)\"\" \"About 
You can put this solution on YOUR website!
.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            In my post,  I will show you the way to solve the problem  MENTALLY,  without using equations.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "The sum of the length and the width is half of the perimeter, i.e. 22 cm.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Half of the sum is 11 cm.  It is the \"mean\" of the length and the width.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let  \"W\"  be the width;  let  \"L\" be the length, and let  d = 11 - W  be the deviation of the width from the mean.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We have then  L = 11 + d;  W = 11 - d;\r\n" );
document.write( "\r\n" );
document.write( "hence,  the area   105 = L*W = (11+d)*(11-d) = 121 - d^2, \r\n" );
document.write( "\r\n" );
document.write( "                   d^2 = 121 - 105 = 16;  d = \"sqrt%2816%29\" = 4 cm.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus the length is  L = 11+4 = 15 cm;  the width is  W = 11-4 = 7 cm.   ANSWER\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "The problem solved MENTALLY, without using equations.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Feel joy having elegant and unexpected solution  (!)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "---------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To see many other similar problems,  solved in this way,  look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Problems on the area and the dimensions of a rectangle\r
\n" ); document.write( "\n" ); document.write( "    - Three methods to find the dimensions of a rectangle when its perimeter and the area are given\r
\n" ); document.write( "\n" ); document.write( "    - Three methods to find the dimensions of a rectangle when its area and the difference of two dimensions are given \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "----------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic
\n" ); document.write( "\"Dimensions and the area of rectangles and circles and their elements\".\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );