Question

determine o valor de x nos feixes de paralelas a/b/c apresentado abaixo

Answer 1

Aplicando o Teorema de Tales , e multiplicando cruzado ( meio pelos extremos)

A) 

$\dfrac{x+4}{4} = \dfrac{12}{3} \\ \\ 12*4=3(x+4) \\ 48=3x+12 \\ 48-12=3x \\ 36=3x \\ \\ x= \dfrac{36}{3} \\ \\ x=12$

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B)

$\dfrac{6}{8} = \dfrac{x}{7-x} \\ \\ 8*x=6*(7-x) \\ \\ 8x=42-6x \\ \\ 8x+6x=42 \\ \\ 14x=42 \\ \\ x= \dfrac{42}{14} \\ \\ x=3$

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C)

$\dfrac{4}{6} = \dfrac{8-x}{x} \\ \\ 4*x=6*(8-x) \\ \\ 4x=48-6x \\ \\ 4x+6x=48 \\ \\ 10x=48 \\ \\ x= \dfrac{48}{10} \\ \\ x=4,8$

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D)


$\dfrac{4}{7} = \dfrac{2x-2}{3x+1} \\ \\ 4*(3x+1)=7*(2x-2) \\ \\ 12x+4=14x-14 \\ \\ 12x-14x=-14-4 \\ \\ -2x=-18*(-1) \\ \\ 2x=18 \\ \\ x= \dfrac{18}{2} \\ \\ x=9$