Question

Nos triângulos abaixo, a medida x indicada em cada um deles são respectivamente:

Answer 1

Explicação passo-a-passo:

a)

$\sf \dfrac{7}{21}=\dfrac{8}{x}$

$\sf 7x=21\cdot8$

$\sf 7x=168$

$\sf x=\dfrac{168}{7}$

$\sf \red{x=24}$

b)

$\sf \dfrac{5}{3}=\dfrac{x}{x-1}$

$\sf 5\cdot(x-1)=3x$

$\sf 5x-5=3x$

$\sf 5x-3x=5$

$\sf 2x=5$

$\sf x=\dfrac{5}{2}$

$\sf \red{x=2,5}$

c)

$\sf \dfrac{3}{x+1}=\dfrac{x}{4}$

$\sf x\cdot(x+1)=3\cdot4$

$\sf x^2+x=12$

$\sf x^2+x-12=0$

$\sf \Delta=1^2-4\cdot1\cdot(-12)$

$\sf \Delta=1+48$

$\sf \Delta=49$

$\sf x=\dfrac{-1\pm\sqrt{49}}{2\cdot1}=\dfrac{-1\pm7}{2}$

$\sf x'=\dfrac{-1+7}~\Rightarrow~x'=\dfrac{6}{2}~\Rightarrow~\red{x'=3}$

$\sf x"=\dfrac{-1-7}{2}~\Rightarrow~x"=\dfrac{-8}{2}~\Rightarrow~\red{x"=-4}$ (não serve)

Logo, x = 3

=> 28; 2,5 e 3