Question

Nas figuras, a // b // c, calcule o valor de x.
Algum MITO ajuda ae ; )​

Answer 1

Explicação passo-a-passo:

Usando o Teorema de Tales:

a)

$\dfrac{x}{4} =\dfrac{9}{18}\\\\ \dfrac{x}{4} =\dfrac{1}{2}\\\\2x=4\\\\x=\dfrac{4}{2}\\\\\boxed{\boxed{x=2} }$

b)

$\dfrac{10}{15} =\dfrac{3x+1}{5x-2} \\\\\dfrac{2}{3} =\dfrac{3x+1}{5x-2}\\\\2.(5x-2)=3.(3x+1)\\\\10x-4=9x+3\\\\10x-9x=3+4\\\\\boxed{\boxed{x=7}}$

c)

$\dfrac{x-5}{x+1} =\dfrac{6}{24}\\\\ \dfrac{x-5}{x+1} =\dfrac{1}{4}\\\\4.(x-5)=x+1\\\\4x-20=x+1\\\\4x-x=1+20\\\\3x=21\\\\x=\dfrac{21}{3}\\\\\boxed{\boxed{x=7}}$

d)

$\dfrac{8}{x+1} =\dfrac{12}{2x-6}\\\\8.(2x-6)=12.(x+1)\\\\16x-48=12x+12\\\\16x-12x=12+48\\\\4x=60\\\\x=\dfrac{60}{4}\\\\\boxed{\boxed{x=15}}$