document.write( "Question 266509: A right triangle has sides of integer length and perimeter 2010 units. The length of the shortest side is equal to one-fifth of the sum of the lengths of the other two sides. What is the area of the triangle? \n" ); document.write( "
Algebra.Com's Answer #195802 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
A right triangle has sides of integer length and perimeter 2010 units. The length of the shortest side is equal to one-fifth of the sum of the lengths of the other two sides. What is the area of the triangle?\r
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "It's a matter of solving this system of equations\r\n" );
document.write( "and substituting in the right triangle area formula\r\n" );
document.write( "\"A=%281%2F2%29ab\"\r\n" );
document.write( "\r\n" );
document.write( "\"system%28a%2Bb%2Bc=2010%2C%0D%0Aa%5E2%2Bb%5E2=c%5E2%2C%0D%0Aa=%281%2F5%29%28b%2Bc%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Clear fractions in the third equation:\r\n" );
document.write( "\r\n" );
document.write( "\"5a=b%2Bc\"\r\n" );
document.write( "\r\n" );
document.write( "Solve the first equation for \"b%2Bc%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"b%2Bc=2010-a\"\r\n" );
document.write( "\r\n" );
document.write( "Therefore\r\n" );
document.write( "\r\n" );
document.write( "\"5a=2010-a\"\r\n" );
document.write( "\r\n" );
document.write( "\"4a=2010\"\r\n" );
document.write( "\r\n" );
document.write( "\"a=335\" \r\n" );
document.write( "\r\n" );
document.write( "Substituting in \r\n" );
document.write( "\r\n" );
document.write( "\"a%2Bb%2Bc=2010\"\r\n" );
document.write( "\r\n" );
document.write( "\"335%2Bb%2Bc=2010\"\r\n" );
document.write( "\r\n" );
document.write( "Solve for c\r\n" );
document.write( "\r\n" );
document.write( "\"c=1675-b\"\r\n" );
document.write( "\r\n" );
document.write( "Substitute that and \"a=335\"\r\n" );
document.write( "in the Pythagorean equation\r\n" );
document.write( "\r\n" );
document.write( "\"a%5E2%2Bb%5E2=c%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"335%5E2%2Bb%5E2=%281675-b%29%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"112225%2Bb%5E2=2805625+-+3350b+%2B+b%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "Cancel the \"b%5E2\"'s\r\n" );
document.write( "\r\n" );
document.write( "\"112225%2Bb%5E2=2805625+-+3350b+%2B+b%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"-26693400=-3350b\"\r\n" );
document.write( "\r\n" );
document.write( "\"3350b=26693400\"\r\n" );
document.write( "\r\n" );
document.write( "\"b=804\"\r\n" );
document.write( "\r\n" );
document.write( "It isn't necessary to find c but we'll do it anyway\r\n" );
document.write( "\r\n" );
document.write( "so we can check if we like.\r\n" );
document.write( "\r\n" );
document.write( "Substitute that in\r\n" );
document.write( "\r\n" );
document.write( "\"c=1675-b\"\r\n" );
document.write( "\r\n" );
document.write( "\"c=1675-804\"\r\n" );
document.write( "\r\n" );
document.write( "\"c=871\"\r\n" );
document.write( "\r\n" );
document.write( "But all we want is the area, so\r\n" );
document.write( "\r\n" );
document.write( "we substitute \"a=335\" and \"b=804\"\r\n" );
document.write( "\r\n" );
document.write( "\"A=%281%2F2%29ab\"\r\n" );
document.write( "\r\n" );
document.write( "\"A=%281%2F2%29%28335%29%28804%29\"\r\n" );
document.write( "\r\n" );
document.write( "A = 134,670 square units.\r\n" );
document.write( "\r\n" );
document.write( "It was not necessary to tell us that the sides are integers.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );