document.write( "Question 1040565: A diagonal of a rhombus, of which the sides are 52cm, is 48cm. What is the length of the other diagonal? (In 1 decimal place)
\n" ); document.write( "Thx. \n" ); document.write( "

Algebra.Com's Answer #655416 by ikleyn(52780) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A diagonal of a rhombus, of which the sides are 52cm, is 48cm. What is the length of the other diagonal?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Solution 1\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Diagonals of a rhombus divide it in four congruent right-angled triangles.\r\n" );
document.write( "By considering one such a triangle, we know its hypotenuse (52 cm) and one of two legs ( = 24 cm). \r\n" );
document.write( "Then we can find the other leg as  =  = 46.13 cm (approximately)\r\n" );
document.write( "So, 46.13 cm is half of the unknown diagonal and 92.26 cm is the entire diagonal length.\r\n" );
document.write( "\r\n" );
document.write( "Answer.  The length of the other diagonal is about 92.26 cm.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solution 2\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "If \"a\" is the length of the rhombus side and \"c\" and \"d\" are the lengths of its diagonals, then\r\n" );
document.write( "\r\n" );
document.write( " = .\r\n" );
document.write( "\r\n" );
document.write( "See the lesson The length of diagonals of a rhombus in this site.\r\n" );
document.write( "\r\n" );
document.write( "Hence,  = , where d is the length of the other diagonal.\r\n" );
document.write( "\r\n" );
document.write( "Then d =  = 92.26 cm (approximately).\r\n" );
document.write( "\r\n" );
document.write( "We have the same answer as in the Solution 1. \r\n" );
document.write( "

\n" ); document.write( " \n" ); document.write( "

\n" );