document.write( "Question 68545: Why can't the length, width, or diagonals of a rectangle be consecutive even numbers? \n" ); document.write( "
Algebra.Com's Answer #48752 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
Assume they are consecutive even numbers:
\n" ); document.write( "1st side = 2n
\n" ); document.write( "2nd side = 2n+2
\n" ); document.write( "diagonal = 2n+4
\n" ); document.write( "----------
\n" ); document.write( "By Pythagoras: (2n+4)^2 = (2n+2)^2+(2n)^2
\n" ); document.write( "4n^2+16n+16 = 4n^2+8n+4 + 4n^2
\n" ); document.write( "Divide thru by 4 to get:
\n" ); document.write( "n^2+4n+4 = n^2+2n+1 + n^2
\n" ); document.write( "n^2 - 2n -3=0
\n" ); document.write( "(n-3)(n+1)=0
\n" ); document.write( "n=3
\n" ); document.write( "1st side = 6
\n" ); document.write( "2nd side = 8
\n" ); document.write( "3rd side = 10
\n" ); document.write( "----------------
\n" ); document.write( "If I understand your conjecture correctly, it is wrong.
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "
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