Question

DETERMINE o valor de x no triângulo abaixo: *

x = 3
x = 6
x = 9
x = 12

Answer 1

Explicação passo-a-passo:

$\sf b^2=a\cdot m$

$\sf 6^2=(x+9)\cdot x$

$\sf 36=x^2+9x$

$\sf x^2+9x-36=0$

$\sf \Delta=9^2-4\cdot1\cdot(-36)$

$\sf \Delta=81+144$

$\sf \Delta=225$

$\sf x=\dfrac{-9\pm\sqrt{225}}{2\cdot1}=\dfrac{-9\pm15}{2}$

$\sf x'=\dfrac{-9+15}{2}~\Rightarrow~x'=\dfrac{6}{2}~\Rightarrow~x'=3$

$\sf x"=\dfrac{-9-15}{2}~\Rightarrow~x"=\dfrac{-24}{2}~\Rightarrow~x"=-12$ (não serve)

Logo, x = 3