O Teorema de Pit\303\241goras
Uma explora\303\247\303\243o deste famoso e fundamental teorema, e suas aplica\303\247\303\265es.
[Dire\303\247\303\265es : Execute primeiramente a se\303\247\303\243o Code Resource. Embora n\303\243o haja nenhum output imediato, essas defini\303\247\303\265es ser\303\243o usadas posteriormente em outro worksheet.]0. 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O Teorema
Todos n\303\263s sabemos como \303\251 um tri\303\242ngulo ret\303\242ngulo, certo?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Ou isso :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O teorema \303\251 esse : (trumpetes por favor....)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Embora ele algumas vezes apare\303\247a disfar\303\247ado :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 2. A Prova
Existe mais de 100 provas que tem sido deixadas nos \303\272ltimos dois mil\303\252nios para esse teorma fundamental. N\303\263s iremos criar um diagrama que pode auxiliar a provar a validade do teorema.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 isso prova o teorma? N\303\263s iremos calcular a \303\241rea para esse diagrama de duas maneiras diferentes.
1. \303\201rea de Partes
Cada um dos quatro tri\303\242ngulos (verde, vermelho, azul, roxo) tem dimens\303\264es a, b, e c.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 2. \303\201rea Total
N\303\263s tamb\303\251m podemos comparar a \303\241rea de uma maneira diferente. O diagrama total \303\251 atualmete um quadrado. A extens\303\243o do lado de um grande quadrado \303\251 a + b, j\303\241 que cada lado do quadrado consiste de um lado menor do tri\303\242ngulo e um grande cateto do tri\303\242ngulo.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 os Dois Tipos de \303\201rea
Agora n\303\263s equacionamos os dois diferentes c\303\241lculos para a \303\241rea, e solucionamos.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY3LUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIipGJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMTY2NjY2N2VtRicvJSdyc3BhY2VHRkctSSNtaUdGJDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnRjItRks2JVEiYkYnRk5GUS1GMzYtUSJ+RidGL0Y2RjlGO0Y9Rj9GQUZDL0ZGUSYwLjBlbUYnL0ZJRlotRjM2LVEiK0YnRi9GNkY5RjtGPUY/RkFGQy9GRlEsMC4yMjIyMjIyZW1GJy9GSUZqbkZWLUZLNiVRImNGJ0ZORlEtRjM2LVEiXkYnRi9GNkY5RjtGPUY/RkFGQy9GRlEsMC4xMTExMTExZW1GJy9GSUZjb0YrRlYtRjM2LVEiPUYnRi9GNkY5RjtGPUY/RkFGQy9GRlEsMC4yNzc3Nzc4ZW1GJy9GSUZpb0ZWLUkobWZlbmNlZEdGJDYkLUYjNidGSkZmbkZTLyUrZXhlY3V0YWJsZUdGOEYvRi9GX29GKy1GMzYtUSI7RidGL0Y2L0Y6RlBGO0Y9Rj9GQUZDRllGam8tRks2I1EhRidGYHBGLw==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEnZXhwYW5kRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEiJUYnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZALUkjbW9HRiQ2LVEiO0YnRkAvJSZmZW5jZUdGPy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0Y/LyUqc3ltbWV0cmljR0Y/LyUobGFyZ2VvcEdGPy8lLm1vdmFibGVsaW1pdHNHRj8vJSdhY2NlbnRHRj8vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJ0Y9RkA=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Voila!...oops....eu quero dizer, "QED" (quo est demonstratum...thus it is demonstrated).
3. Encontrando os Lados dos Tri\303\242ngulos Ret\303\242ngulos
dados dois lados quaisquer de um tri\303\242ngulo ret\303\242ngulo \303\251 poss\303\255vel encontrar o terceiro lado usando esta f\303\263rmula. A \303\272nica chave para usar a f\303\263rmula \303\251 substitu\303\255-la apropriadamente.Apenas lembre-se que c, a hipotenusa, \303\251 o lado maior do tri\303\242ngulo, e seu quadrado \303\251 igual a soma dos quadrados dos outros dois.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 Exemplo 3.1: Um tri\303\242ngulo ret\303\242ngulo tem catetos de lados 7 e 24, encontre a hipotenusa
Nesse caso, nos deram os dois catetos - os dois lados menores, a e b.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVElc3Vic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYpLUkjbW9HRiQ2LVEifkYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRLUY2NiYtRiM2MC1GLDYlUSJhRidGL0YyRjotRjs2LVEiPUYnRj5GQEZDRkVGR0ZJRktGTS9GUFEsMC4yNzc3Nzc4ZW1GJy9GU0ZpbkY6LUkjbW5HRiQ2JFEiNUYnRj4tRjs2LVEiLEYnRj5GQC9GREYxRkVGR0ZJRktGTUZPL0ZTUSwwLjMzMzMzMzNlbUYnRjotRiw2JVEiYkYnRi9GMkY6RmVuRjotRlxvNiRRIzEyRidGPi8lK2V4ZWN1dGFibGVHRkJGPkY+LyUlb3BlbkdRInxmckYnLyUmY2xvc2VHUSJ8aHJGJ0Zfb0Y6LUYsNiVRJVB5dGhGJ0YvRjJGW3BGPkY+LUY7Ni1RIjtGJ0Y+RkBGYm9GRUZHRklGS0ZNRk9Gam4tSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdGUS8lJmRlcHRoR0ZecS8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GanA2JkZccUZfcUZhcS9GZHFRJWF1dG9GJy1GLDYjUSFGJ0ZbcEY+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYzLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJ0YrLUYsNi1RIj1GJ0YvRjJGNUY3RjlGO0Y9Rj8vRkJRLDAuMjc3Nzc3OGVtRicvRkVGU0YrLUYsNi1RIidGJ0YvRjJGNUY3RjlGO0Y9Rj8vRkJRLDAuMTExMTExMWVtRidGRC1GRzYlUSVzcXJ0RicvRktGNEYvLUkobWZlbmNlZEdGJDYkLUYjNiUtSSNtbkdGJDYkUSQxNjlGJ0YvLyUrZXhlY3V0YWJsZUdGNEYvRi9GVS1GLDYtUSI7RidGL0YyL0Y2RkxGN0Y5RjtGPUY/RkFGVC1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR0ZDLyUmZGVwdGhHRlxwLyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUZobzYmRmpvRl1wRl9wL0ZicFElYXV0b0YnLUZHNiVRJ2V4cGFuZEYnRkpGTS1GaW42JC1GIzYlLUZHNiVRIiVGJ0ZKRk1GYW9GL0YvRmNvRmFvRi8=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVErUnRUcmlQbG90MkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYnLUkjbW5HRiQ2JFEiNUYnL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkYvJSpzeW1tZXRyaWNHRkYvJShsYXJnZW9wR0ZGLyUubW92YWJsZWxpbWl0c0dGRi8lJ2FjY2VudEdGRi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUY7NiRRIzEyRidGPi8lK2V4ZWN1dGFibGVHRkZGPkY+LUZBNi1RIjtGJ0Y+RkRGR0ZJRktGTUZPRlFGUy9GV1EsMC4yNzc3Nzc4ZW1GJ0ZmbkY+Isso se adapta a um inteiro, mas habitualmente, existe uma ra\303\255z quadrada envolvida de uma maneira ou outra.
Exemplo 3.2: Um tri\303\242ngulo ret\303\242ngulo tem catetos de lado 2 e 3, encontre a hipotenusa
Nesse caso, nos deram os dois catetos - os dois lados menores, a e b.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVElc3Vic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYpLUkjbW9HRiQ2LVEifkYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRLUY2NiYtRiM2MC1GLDYlUSJhRidGL0YyRjotRjs2LVEiPUYnRj5GQEZDRkVGR0ZJRktGTS9GUFEsMC4yNzc3Nzc4ZW1GJy9GU0ZpbkY6LUkjbW5HRiQ2JFEiMkYnRj4tRjs2LVEiLEYnRj5GQC9GREYxRkVGR0ZJRktGTUZPL0ZTUSwwLjMzMzMzMzNlbUYnRjotRiw2JVEiYkYnRi9GMkY6RmVuRjotRlxvNiRRIjNGJ0Y+LyUrZXhlY3V0YWJsZUdGQkY+Rj4vJSVvcGVuR1EifGZyRicvJSZjbG9zZUdRInxockYnRl9vRjotRiw2JVElUHl0aEYnRi9GMkZbcEY+Rj4tRjs2LVEiO0YnRj5GQEZib0ZFRkdGSUZLRk1GT0ZqbkZbcEY+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjI3Nzc3NzhlbUYnL0ZORlNGNS1GLDYlUSVzcXJ0RicvRjBGPUY5LUkobWZlbmNlZEdGJDYkLUYjNiUtSSNtbkdGJDYkUSMxM0YnRjkvJStleGVjdXRhYmxlR0Y9RjlGOS1GNjYtUSI7RidGOUY7L0Y/RjFGQEZCRkRGRkZIRkpGVEZcb0Y5LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDRistSSNtaUdGJDYlUStSdFRyaVBsb3QyRicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNictSSNtbkdGJDYkUSIyRidGLy1GLDYtUSIsRidGL0YyL0Y2RkxGN0Y5RjtGPUY/RkEvRkVRLDAuMzMzMzMzM2VtRictRlU2JFEiM0YnRi8vJStleGVjdXRhYmxlR0Y0Ri9GLy1GLDYtUSI7RidGL0YyRmVuRjdGOUY7Rj1GP0ZBL0ZFUSwwLjI3Nzc3NzhlbUYnRltvRi8=Aqui est\303\241 a outra varia\303\247\303\243o - dada a hipotenusa e um cateto.
Exemplo 3.3: Um tri\303\242ngulo reto tem um catetode 10 polegadas e hipotenusa de 15 polegadas, encontre o outro lado
Nesse caso, nos deram os dois lados - a e b.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. Os Conhecidos Tri\303\242ngulos Ret\303\242ngulos
Existem duas fam\303\255lias muito comuns de tri\303\242ngulos ret\303\242ngulos, as quais s\303\243o bem conceituadas.
45-45-90 Tri\303\242ngulo
Quando dois catetos s\303\243o iguais, os dois \303\242ngulos da base s\303\243o iguais tamb\303\251m - 45 graus cada.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A hipotenusa \303\251 sempre LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JUYrLUkmbXNxcnRHRiQ2Iy1GIzYkLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Y6RjotSSNtb0dGJDYtUSJ+RidGOi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQy8lKXN0cmV0Y2h5R0ZDLyUqc3ltbWV0cmljR0ZDLyUobGFyZ2VvcEdGQy8lLm1vdmFibGVsaW1pdHNHRkMvJSdhY2NlbnRHRkMvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZSLyUrZXhlY3V0YWJsZUdGQ0Y6 vezes o lado de cada um dos dois catetos em um tri\303\242ngulo 45-45-90.
O outro \303\242ngulo comum \303\251 esse.
30-60-90 Tri\303\242ngulo
Esse tipo de tri\303\242ngulo pode ser considerado como parte de um tri\303\242ngulo equil\303\241tero, e ent\303\243o a base menor \303\251 a metade da hipotenusa. Saber isso nos permite expressar o terceiro lado (o cateto maior) em termos dos outros dois.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Isso fornece a rela\303\247\303\243o entre os lados : 1 : LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictSSZtc3FydEdGJDYjLUYjNiQtSSNtbkdGJDYkUSIzRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjhGOA== : 2
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
Frequentemente n\303\263s vemos esse tipo de tri\303\242ngulo expressado nessa forma, onde a hipotenusa \303\251 1. 1/2 : LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictSSZtc3FydEdGJDYjLUYjNiQtSSNtbkdGJDYkUSIzRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjhGOA==/2 : 1
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVElc3Vic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYuLUYsNiVRInhGJ0YvRjItSSNtb0dGJDYtUSJ+RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlQtRj42LVEiPUYnRkFGQ0ZGRkhGSkZMRk5GUC9GU1EsMC4yNzc3Nzc4ZW1GJy9GVkZlbkY9LUkjbW5HRiQ2JFEiMUYnRkEtRj42LVEiL0YnRkFGQ0ZGL0ZJRjFGSkZMRk5GUC9GU1EsMC4xNjY2NjY3ZW1GJy9GVkZgby1GaG42JFEiMkYnRkEtRj42LVEiLEYnRkFGQy9GR0YxRkhGSkZMRk5GUEZSL0ZWUSwwLjMzMzMzMzNlbUYnRj0tRiw2JVEnVHJpMzY5RidGL0YyLyUrZXhlY3V0YWJsZUdGRUZBRkEtRj42LVEiO0YnRkFGQ0Zob0ZIRkpGTEZORlBGUkZmbi1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR0ZULyUmZGVwdGhHRmhwLyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUZkcDYmRmZwRmlwRltxL0ZecVElYXV0b0YnLUYsNiNRIUYnRl5wRkE=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVErUnRUcmlQbG90MkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYqLUkjbW5HRiQ2JFEiN0YnL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkYvJSpzeW1tZXRyaWNHRkYvJShsYXJnZW9wR0ZGLyUubW92YWJsZWxpbWl0c0dGRi8lJ2FjY2VudEdGRi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnRjotRkE2LVEiKkYnRj5GRC9GSEZGRklGS0ZNRk9GUS9GVFEsMC4xNjY2NjY3ZW1GJy9GV0Zobi1GLDYlUSVzcXJ0RicvRjBGRkY+LUY2NiQtRiM2JS1GOzYkUSIzRidGPi8lK2V4ZWN1dGFibGVHRkZGPkY+RmVvRj5GPi1GQTYtUSI7RidGPkZERkdGSUZLRk1GT0ZRRlMvRldRLDAuMjc3Nzc3OGVtRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdGVS8lJmRlcHRoR0ZhcC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GXXA2JkZfcEZicEZkcC9GZ3BRJWF1dG9GJy1GLDYjUSFGJ0Zlb0Y+Por favor, d\303\252 uma olhada na worksheet "Triplos Pitag\303\263ricos" para obter mais materiais interessantes.