document.write( "Question 1181876: The perimeter of a rectangle is 120cm. The area of the rectangle is 864cm^2. Determine the length and width of the rectangle. \n" ); document.write( "

Algebra.Com's Answer #811823 by ikleyn(52778) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "The perimeter of a rectangle is 120cm. The area of the rectangle is 864cm^2.
\n" ); document.write( "Determine the length and width of the rectangle.
\n" ); document.write( "~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " The standard algebra solution is as follows.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let w be the width length, in centimeters.\r\n" );
document.write( "\r\n" );
document.write( "Then the length is  (120/2-w) = 60-w  centimeters long.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The area is  w*(60-w);  therefore, the \"area\" equation is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    w*(60-w) = 864.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Write it in the standard form quadratic equation\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    w^2 - 60w + 864 = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Use the quadratic formula\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     =  =  =  = 30 +- 6.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "One answer is  24 cm for the width and 36 cm for the length.\r\n" );
document.write( "\r\n" );
document.write( "The other answer is 36 cm for the width and 24 cm for the length.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The dimensions of the rectangle are  36 cm  and  24 cm.\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " The standard solution is completed.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " Now I will show you a non-standard one.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "The sum of the width and the length is 120/2 = 60 centimeters.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Notice that the mean of the width and the length values is the number of   = 30.  \r\n" );
document.write( "This number is exactly half-way between the length and the width values.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So,  the length = 30+x,  while the width = 30-x centimeters, where x is some unknown value.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since the area of the rectangle is 864 cm^2 (given), you have this equation\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    (30+x)*(30-x) = 864,\r\n" );
document.write( "\r\n" );
document.write( "or\r\n" );
document.write( "\r\n" );
document.write( "    900 - x^2 = 864,\r\n" );
document.write( "\r\n" );
document.write( "     x^2      = 900 - 864\r\n" );
document.write( "\r\n" );
document.write( "     x^2      = 36\r\n" );
document.write( "\r\n" );
document.write( "      x       =  = 6.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus the dimensions of the rectangle are  30+6 = 36 cm  and  30-6 = 24 cm.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You get the same answer.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved (in two ways, and the second way is practically MENTAL solution).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );