document.write( "Question 1019325: the medians of a right triangle that are drawn from the vertices of the acute angles have lengths of 2 square root 13 and square root 73. find the lengths of the hypotenuse. \n" ); document.write( "

Algebra.Com's Answer #635326 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "The medians of a right triangle that are drawn from the vertices of the acute angles have lengths of 2 square root 13 and square root 73. Find the lengths of the hypotenuse.
\n" ); document.write( "---------------------------------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Answer. The length of the hypotenuse is 10 units.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Solution\r\n" );
document.write( "\r\n" );
document.write( "We will use this property of a median, which is valid for any triangle:\r\n" );
document.write( "\r\n" );
document.write( "  In a triangle with the sides a, b and c, the median drawn to the side c has the length  = .\r\n" );
document.write( "\r\n" );
document.write( "See the lesson The length of a median of a triangle in this site.\r\n" );
document.write( "\r\n" );
document.write( "Next, let us apply the property to a right-angled triangle, whose legs are a and b units long and the hypotenuse is c units long.\r\n" );
document.write( "\r\n" );
document.write( "For the medians    and    drawn to the legs a and b respectively, we will have\r\n" );
document.write( "\r\n" );
document.write( " = ,   = . \r\n" );
document.write( "\r\n" );
document.write( "Therefore,\r\n" );
document.write( "\r\n" );
document.write( " +  =  +  =  = .\r\n" );
document.write( "\r\n" );
document.write( "Since for the right-angled triangle  = , you can rewrite the above equality in the form\r\n" );
document.write( "\r\n" );
document.write( " +  =  = .\r\n" );
document.write( "\r\n" );
document.write( "Now substitute the given data   =   and   = . You will get\r\n" );
document.write( "\r\n" );
document.write( " =  = .\r\n" );
document.write( "\r\n" );
document.write( "It implies   =  = .\r\n" );
document.write( "\r\n" );
document.write( "Hence, c = 10.\r\n" );
document.write( "\r\n" );
document.write( "The problem is solved.\r\n" );
document.write( "

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

\n" );