Algebra.Com's Answer #748198 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
.
\n" );
document.write( "The perimeter of a right triangle is 42 and the sum of the squares of its sides is 722. Determine the area of the right triangle.
\n" );
document.write( "~~~~~~~~~~~~~~~~\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "\r\n" );
document.write( "a + b + c = 42 (1)\r\n" );
document.write( "a^2 + b^2 = c^2 (2)\r\n" );
document.write( "a^2 + b^2 + c^2 = 722 (3)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From (2) and (3)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "2c^2 = 722 ====> c^2 = 722/2 = 361\r\n" );
document.write( "\r\n" );
document.write( "c =  = 19.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now substitute c= 19 and c^2 = 361 into eq(1) and eq(2). You will get\r\n" );
document.write( "\r\n" );
document.write( "a + b = 23 (1')\r\n" );
document.write( "a^2 + b^2 = 361 (2')\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now square both sides of (1'). Keep (2') as is. You will get\r\n" );
document.write( "\r\n" );
document.write( "a^2 + 2ab + b^2 = 23^2 = 529 (1'')\r\n" );
document.write( "a^2 + b^2 = 361 (2'')\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Subtract (2'') from (1''). You will get\r\n" );
document.write( "\r\n" );
document.write( "2ab = 529 - 361 = 168.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now the area of the triangle =  =  = 42. 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( " |