Question 334425: find the number of sides of a polygon with diagonals equal to forty-five less than ten times the number of sides Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! find the number of sides of a polygon with diagonals equal to forty-five less than ten times the number of sides
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Let the number of sides be "n"
Then number of diagonals is nC2-n
= [n(n-1)/2]-n
= [n^2-n-2n]/2
= (n^2-3n)/2
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Equation:
[n^2-3n]/2 = 10n-45
n^2-3n = 20n-90
n^2-23n+90 = 0
(n-5)(n-18) = 0
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number of sides = 5 or number of sides = 18
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Cheers,
Stan H.
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