Considere os triângulos ABC e CDE da figura a seguir Calcule a+b+c.... Pergunta de ideia deSayori

January 2020 1 56 Report

Considere os triângulos ABC e CDE da figura a seguir
Calcule a+b+c

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gabrieldoile Primeiro calcularemos o valor de a:

$5^{2} = 4^{2} +a^{2} \\ 25 = 16 + a^{2} \\ a^{2} = 9 \\ a= \sqrt{9} \\ a = 3$

Logo temos o seguinte para b:

$a + b = 12 \\ 3 + b = 12 \\ b = 12-3 \\ b = 9$

Logo temos o valor de c:

$c^{2} = b^{2} + 12^{2} \\ c^{2} = 9^{2} + 12^{2} \\ c^{2} = 81 + 144 \\ c = \sqrt{255} \\ c = 15$

Logo temos:

$a + b + c = 3 + 9 +15 = 27$

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