Question

relações métricas: calcule as medidas desconhecidas

Answer 1

$3^2=5\cdot m\\\\9=5m\\\\\boxed{m=\frac{9}{5}}$

Utilizando o Teorema de Pitágoras no triângulo inteiro:

$5^2=3^2+x^2\\\\25=9+x^2\\\\x^2=16\\\\\boxed{x=4}$

Utilizando Teorema de Pitágoras no triângulo esquerdo:

$3^2=m^2+h^2\\\\9=(\,\frac{9}{5})\,+h^2\\\\9=\frac{81}{25}+h^2\\\\h^2=9-\frac{81}{25}\\\\h^2=\frac{25\cdot9}{25}-\frac{81}{25}\\\\h^2=\frac{144}{25}\\\\\boxed{h=\frac{12}{5}}$
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$h^2=m\cdot n$

$(\,\frac{12}{5})^\,^2=(\,\frac{9}{5})\,^2\cdot n^2$

$\frac{144}{25}=\frac{81}{25}\cdot n^2$

$n^2=\frac{144}{25}\cdot\frac{25}{81}$

$n^2=\frac{144}{81}$

$n=\frac{12}{9}$

$\boxed{n=\frac{4}{3}}$