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