document.write( "Question 1157422: The figure below consists of a smaller square inside a larger one. The difference in their areas (the shaded part) is 17 cm². The sum of the perimeters of the two squares is 68 cm. How long are the sides of the larger square? \n" ); document.write( "

Algebra.Com's Answer #780289 by ikleyn(52786) $\"\"$ $\"About$

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

\r\n" );
document.write( "\r\n" );
document.write( "From the condition, you have 2 equations\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    x + y     = 17.        (1)\r\n" );
document.write( "\r\n" );
document.write( "    x^2 - y^2 = 17.        (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Factor equation (2)\r\n" );
document.write( "\r\n" );
document.write( "    (x+y)*(x-y) = 17.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Replace here x+y by 17, based on equation (1).  You will get\r\n" );
document.write( "\r\n" );
document.write( "    17*(x-y) = 17,   or  x-y = 1.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus, instead of equations (1) and (2), you have much simpler system\r\n" );
document.write( "\r\n" );
document.write( "    x + y = 17    (3)\r\n" );
document.write( "\r\n" );
document.write( "    x - y =  1    (4)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Add the equations, and get 2x - 19,  x = 9.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence,  y = 17-9 = 8.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The sides of the square are 9 cm  and  8 cm.\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( "

\n" );