document.write( "Question 483111: How do you find the side lengths of an isosceles triangle if you just have the other 2 side lengths and not the perimeter? \n" ); document.write( "

Algebra.Com's Answer #330626 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
How do you find the side lengths of an isosceles triangle if you just have the other 2 side lengths and not the perimeter?
\n" ); document.write( "

\r\n" );
document.write( "Since the triangle is isosceles, the third side has to have one of the\r\n" );
document.write( "two given lengths.\r\n" );
document.write( "\r\n" );
document.write( "Sometimes there are \r\n" );
document.write( "\r\n" );
document.write( "1. Infinitely many solutions.\r\n" );
document.write( "\r\n" );
document.write( "Sometimes there are \r\n" );
document.write( "\r\n" );
document.write( "2.  two solutions.\r\n" );
document.write( "\r\n" );
document.write( "Sometimes there is \r\n" );
document.write( "\r\n" );
document.write( "3.  just one solution.\r\n" );
document.write( "\r\n" );
document.write( "Case 1 is when the two given sides are equal in length.\r\n" );
document.write( "Then the two given sides are the legs, and the base can have any \r\n" );
document.write( "positive length less than twice the length of one of the given \r\n" );
document.write( "sides.  That gives an infinite number of solutions.\r\n" );
document.write( "\r\n" );
document.write( "For the other two cases.  let S be the shorter length and\r\n" );
document.write( "L be the longer.  \r\n" );
document.write( "\r\n" );
document.write( "There is always a solution in which the two legs have the longer \r\n" );
document.write( "length L, and the base has the shorter length S.\r\n" );
document.write( "\r\n" );
document.write( "There is sometimes a second solution where the two legs have \r\n" );
document.write( "length S. If the triangular inequality holds with the legs having\r\n" );
document.write( "length S, then\r\n" );
document.write( "\r\n" );
document.write( "S+S > L\r\n" );
document.write( " 2S > L\r\n" );
document.write( "  S > \r\n" );
document.write( "\r\n" );
document.write( "then there is a second solution.\r\n" );
document.write( "\r\n" );
document.write( "So we can say:\r\n" );
document.write( "\r\n" );
document.write( "1. If the two given lengths are equal, there are infinitely many solutions.\r\n" );
document.write( "\r\n" );
document.write( "2. If the shorter given length is greater than half the longer given\r\n" );
document.write( "   length, there are 2 solutions.\r\n" );
document.write( "\r\n" );
document.write( "3. If the shorter given length is equal to or less than one-half the longer\r\n" );
document.write( "   given length, there is only 1 solutions.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

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

\n" );