Question

de acordo com os dados, determine o valor de x+y+z​

Answer 1

Explicação passo-a-passo:

Pelo Teorema de Tales:

=> Valor de z

$\sf \dfrac{z}{2}=\dfrac{11}{9}$

$\sf 9z=2\cdot11$

$\sf 9z=22$

$\sf \red{z=\dfrac{22}{9}}$

=> Valor de y

$\sf \dfrac{y}{3}=\dfrac{9}{11}$

$\sf 11y=3\cdot9$

$\sf 11y=27$

$\sf \red{y=\dfrac{27}{11}}$

=> Valor de x

$\sf \dfrac{x}{y}=\dfrac{7}{3}$

$\sf \dfrac{x}{\frac{27}{11}}=\dfrac{7}{3}$

$\sf 3x=7\cdot\dfrac{27}{11}$

$\sf 3x=\dfrac{189}{11}$

$\sf x=\dfrac{\frac{189}{11}}{3}$

$\sf x=\dfrac{189}{11}\cdot\dfrac{1}{3}$

$\sf x=\dfrac{189}{33}$

$\sf \red{x=\dfrac{63}{11}}$

Logo:

$\sf x+y+z=\dfrac{63}{11}+\dfrac{27}{11}+\dfrac{22}{9}$

$\sf x+y+z=\dfrac{90}{11}+\dfrac{22}{9}$

$\sf x+y+z=\dfrac{810+242}{99}$

$\sf \red{x+y+z=\dfrac{1052}{99}}$