A polygon has 35 diagonals. How many sides does it have?

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15-07-2014
Mathematics

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A polygon has 35 diagonals. How many sides does it have?

Sagot :

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Konrad509idn Konrad509idn · Answer 1 · 2014-07-15T13:07:16-04:00

Konrad509idn Konrad509idn

15-07-2014

[tex]d=35\\ d=\frac{n(n-3)}{2}\\ d=\frac{n(n-3)}{2}\\35=\frac{n(n-3)}{2}\\ 70=n^2-3n\\ n^2-3n-70=0\\ n^2-10n+7n-70=0\\ n(n-10)+7(n-10)=0\\ (n+7)(n-10)=0\\ n=-7 \vee n=10\\\\ n=10 [/tex]

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