document.write( "Question 1125927: The lengths of the sides of a triangle are 13cm, 37cm and 40cm. Find the length of the altitude to the longest side, in cm... \n" ); document.write( "

Algebra.Com's Answer #742299 by ikleyn(52786) $\"\"$ $\"About$

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

\r\n" );
document.write( "\r\n" );
document.write( "The standard strategy for solving such problems is to calculate the area of the triangle using the Heron's formula;\r\n" );
document.write( "\r\n" );
document.write( "then to divide the area by the half of the base.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The perimeter of the triangle is  13 + 37 + 40 = 90 cm;  hence, the semi-perimeter is  90/2 = 45 cm.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "By the Heron's formula, area of the triangle is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    A =  =  =  =  = 3*5*16 = 240 cm^2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then the length of the altitude to the longest side  =  =  = 12 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" );