document.write( "Question 1106697: A wooden plaque, square in shape, has a bronze inlay, square in shape, in the center. A wooden strip of uniform width surrounds the bronze square. The ratio of the bronze area to the wooden area is 25 to 39. Calculate width of the wooden strip.\r
\n" ); document.write( "\n" ); document.write( "Let x = length of side of plaque.\r
\n" ); document.write( "\n" ); document.write( "Let y = length of side of inlay.\r
\n" ); document.write( "\n" ); document.write( "Let w = width of wooden strip.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Area of square = s^2.\r
\n" ); document.write( "\n" ); document.write( "Area of plaque = x^2.\r
\n" ); document.write( "\n" ); document.write( "Area of inlay = y^2.\r
\n" ); document.write( "\n" ); document.write( "Not sure how to continue. Non-homework. \n" ); document.write( "

Algebra.Com's Answer #721685 by ikleyn(52781) $\"\"$ $\"About$

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

\r\n" );
document.write( " = \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is what you are given, according to the condition.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify:\r\n" );
document.write( "\r\n" );
document.write( " = ,\r\n" );
document.write( "\r\n" );
document.write( " = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus you have this quadratic equation for the RATIO  .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You can solve the equation and find this ratio from there.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Notice that the ratio is  THE ONLY thing  which you can obtain from the given data,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "          and  you can not obtain dimensions separately,  because there is NO sufficient data for it.\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To get better understanding of this fact, imagine two geometrically similar configurations.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The \"ratio correlations\" will be the same, but the real/actual dimensions will be different.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "------------------
\n" ); document.write( "For similar problems, see the lesson\r
\n" ); document.write( "\n" ); document.write( " - Problems on the area and the dimensions of a rectangle surrounded by a strip\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );