Question

aplicando as relações métricas nos triângulos retângulos abaixo , determine o valor da incógnita
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Answer 1

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$\tt a)~\huge\boxed{\boxed{\boxed{\boxed{\sf a=2+4=6\checkmark}}}}\\\sf h^2=2\cdot4\\\sf h=\sqrt{2\cdot4}\\\huge\boxed{\boxed{\boxed{\boxed{\sf h=2\sqrt{2}\checkmark}}}}\\\sf c^2=6\cdot2\\\sf c^2=4\cdot3\\\sf c=\sqrt{4\cdot3}\\\huge\boxed{\boxed{\boxed{\boxed{\boxed{\sf c=2\sqrt{3}\checkmark}}}}}\\\sf a\cdot h=b\cdot c\implies b=\dfrac{a\cdot h}{c}\\\sf b=\dfrac{6\cdot\diagup\!\!\!\!2\sqrt{2}}{\diagup\!\!\!\!2\sqrt{3}}\\\sf b=\dfrac{6\sqrt{6}}{3}\\\huge\boxed{\boxed{\boxed{\boxed{\boxed{\sf b=2\sqrt{6}}}}}}$

$\tt b)~\huge\boxed{\boxed{\boxed{\boxed{\sf a=18+32=50\checkmark}}}}\\\sf h^2=18\cdot32\\\sf h^2=9\cdot2\cdot16\cdot2=9\cdot16\cdot4\\\sf h=\sqrt{9\cdot16\cdot4}\\\sf h=3\cdot4\cdot2\\\huge\boxed{\boxed{\boxed{\boxed{\sf h=24\checkmark}}}}}\\\sf b^2=50\cdot18\\\sf b^2=900\\\sf b=\sqrt{900}\\\huge\boxed{\boxed{\boxed{\boxed{\sf b=30\checkmark}}}}\\\sf c=\dfrac{a\cdot h}{b}\\\sf c=\dfrac{5\diagdown\!\!\!\!0\cdot\diagup\!\!\!\!\!24}{\diagup\!\!\!3\diagdown\!\!\!\!0}\\\sf c=5\cdot8$

$\Huge\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\sf c=40\checkmark}}}}}}}$