alguém pode me ajudar neste dever de matemática?
1.Quantos lados tem o polígono em que o número de diagonais é igual ao dobro do número de lados?
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Boa noite Silva!
Solução!
![d= \dfrac{n(n-3)}{2}\\\\\\\\
\boxed{d=2n}\\\\\\\\
2n= \dfrac{n(n-3)}{2}\\\\\\\
4n= n^{2}-3n\\\\\\
n^{2}-3n-4n=0\\\\\
n^{2}-3n-4n=0\\\\\
n^{2}-7n=0\\\\\ \\\\\
n(n-7)=0\\\\\
n=0\\\\\
\boxed{n=7}\\\\\\\\
7~~lados\\\\\\\\
\boxed{Resposta:~~O~~poligono~~e~~~~um~~heptagono}](https://tex.z-dn.net/?f=d%3D+%5Cdfrac%7Bn%28n-3%29%7D%7B2%7D%5C%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7Bd%3D2n%7D%5C%5C%5C%5C%5C%5C%5C%5C%0A2n%3D+%5Cdfrac%7Bn%28n-3%29%7D%7B2%7D%5C%5C%5C%5C%5C%5C%5C%0A4n%3D+n%5E%7B2%7D-3n%5C%5C%5C%5C%5C%5C%0An%5E%7B2%7D-3n-4n%3D0%5C%5C%5C%5C%5C%0An%5E%7B2%7D-3n-4n%3D0%5C%5C%5C%5C%5C%0A+n%5E%7B2%7D-7n%3D0%5C%5C%5C%5C%5C+%5C%5C%5C%5C%5C%0An%28n-7%29%3D0%5C%5C%5C%5C%5C%0An%3D0%5C%5C%5C%5C%5C%0A%5Cboxed%7Bn%3D7%7D%5C%5C%5C%5C%5C%5C%5C%5C%0A7%7E%7Elados%5C%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BResposta%3A%7E%7EO%7E%7Epoligono%7E%7Ee%7E%7E%7E%7Eum%7E%7Eheptagono%7D "d= \dfrac{n(n-3)}{2}\\\\\\\\
\boxed{d=2n}\\\\\\\\
2n= \dfrac{n(n-3)}{2}\\\\\\\
4n= n^{2}-3n\\\\\\
n^{2}-3n-4n=0\\\\\
n^{2}-3n-4n=0\\\\\
n^{2}-7n=0\\\\\ \\\\\
n(n-7)=0\\\\\
n=0\\\\\
\boxed{n=7}\\\\\\\\
7~~lados\\\\\\\\
\boxed{Resposta:~~O~~poligono~~e~~~~um~~heptagono}")
Boa noite!
Bons estudos!
Solução!
Boa noite!
Bons estudos!
45silva2016:
obrigado! boa noite!!!!!
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