um retângulo mede 4cm de largura e diagonal 4 raiz quadrada de 5cm.qual é a altura desse retângulo
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Boa noite!
Solução!
É só aplicar o teorema de Pitágoras!
![Diagonal=4 \sqrt{5}~cm\\\\\
Largura=4~cm\\\\\
Altura=?\\\\\\\\\
(Diagonal)^{2}=(Largura)^{2}+(Altura)^{2}\\\\\\\
(4 \sqrt{5} )^{2}=(4)^{2}+(Altura)^{2}\\\\\\\
16.5=16+(Altura)^{2}\\\\\\\
80=16+(Altura)^{2}\\\\\\\
80-16=(Altura)^{2}\\\\\\\
64=(Altura)^{2}\\\\\\\
(Altura)= \sqrt{64} \\\\\\\
\boxed{Altura= 8cm}](https://tex.z-dn.net/?f=Diagonal%3D4+%5Csqrt%7B5%7D%7Ecm%5C%5C%5C%5C%5C%0ALargura%3D4%7Ecm%5C%5C%5C%5C%5C%0AAltura%3D%3F%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A%28Diagonal%29%5E%7B2%7D%3D%28Largura%29%5E%7B2%7D%2B%28Altura%29%5E%7B2%7D%5C%5C%5C%5C%5C%5C%5C%0A%284+%5Csqrt%7B5%7D+%29%5E%7B2%7D%3D%284%29%5E%7B2%7D%2B%28Altura%29%5E%7B2%7D%5C%5C%5C%5C%5C%5C%5C%0A16.5%3D16%2B%28Altura%29%5E%7B2%7D%5C%5C%5C%5C%5C%5C%5C%0A80%3D16%2B%28Altura%29%5E%7B2%7D%5C%5C%5C%5C%5C%5C%5C%0A80-16%3D%28Altura%29%5E%7B2%7D%5C%5C%5C%5C%5C%5C%5C+++%0A64%3D%28Altura%29%5E%7B2%7D%5C%5C%5C%5C%5C%5C%5C+%0A%28Altura%29%3D+%5Csqrt%7B64%7D+%5C%5C%5C%5C%5C%5C%5C++%0A%5Cboxed%7BAltura%3D+8cm%7D+%0A+ "Diagonal=4 \sqrt{5}~cm\\\\\
Largura=4~cm\\\\\
Altura=?\\\\\\\\\
(Diagonal)^{2}=(Largura)^{2}+(Altura)^{2}\\\\\\\
(4 \sqrt{5} )^{2}=(4)^{2}+(Altura)^{2}\\\\\\\
16.5=16+(Altura)^{2}\\\\\\\
80=16+(Altura)^{2}\\\\\\\
80-16=(Altura)^{2}\\\\\\\
64=(Altura)^{2}\\\\\\\
(Altura)= \sqrt{64} \\\\\\\
\boxed{Altura= 8cm}")
Boa noite!
Bons estudos!
Solução!
É só aplicar o teorema de Pitágoras!
Boa noite!
Bons estudos!
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