document.write( "Question 174025: The lenght of the sides of a triangle are consecutive even integers. Find the lenght of the longest side if it is 22 units shorter that the perimeter. \n" ); document.write( "

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Ok, well if all the sides are consecutive even integers they can be written as follows:\r
\n" ); document.write( "\n" ); document.write( "2n
\n" ); document.write( "2n + 2
\n" ); document.write( "2n + 4\r
\n" ); document.write( "\n" ); document.write( "So, the perimeter is 2n + (2n + 2) + (2n + 4) or 6n + 6\r
\n" ); document.write( "\n" ); document.write( "Since the longest side is 2n + 4 and it is 22 units shorter than the perimeter we have,\r
\n" ); document.write( "\n" ); document.write( "(2n + 4) + 22 = 6n + 6
\n" ); document.write( "2n + 26 = 6n + 6
\n" ); document.write( "2n = 6n - 20
\n" ); document.write( "-4n = -20
\n" ); document.write( "n = 5\r
\n" ); document.write( "\n" ); document.write( "The longest side is 2n + 4 and n = 5 so 2(5) + 4 = 14 is the longest side.\r
\n" ); document.write( "\n" ); document.write( "Thus, the triangle has sides, 10, 12, 14. \n" ); document.write( "

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