document.write( "Question 744559: A square region with a side length of 2 inches lies within another, larger square region as shown above. If the larger square region has an area twice that of the smaller square region, then how much larger is the diagonal of the large square region than the diagonal of the small square region? \n" ); document.write( "

Algebra.Com's Answer #852577 by ikleyn(53142) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A square region with a side length of 2 inches lies within another, larger square region as shown above.
\n" ); document.write( "If the larger square region has an area twice that of the smaller square region, then how much larger
\n" ); document.write( "is the diagonal of the large square region than the diagonal of the small square region?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Both squares are similar figures geometrically (as any two squares).\r\n" );
document.write( "\r\n" );
document.write( "We know that the area ratio is 2 (the greater to the smaller).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence, the similarity coefficient (linear) is , the greater to the smaller.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It means that the diagonal of the greater square is  times as long as that of the smaller square.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The diagonal of the smaller square is  =  =  cm.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence, the diagonal of the greater square is   = 2*2 = 4 cm.    \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To determine, how much it is longer, subtract the two numbers  \r\n" );
document.write( "\r\n" );
document.write( "     = 1.1716  cm  (rounded).    ANSWER\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" ); document.write( "

\n" );