Question

determine o valor de x ​

Answer 1

Resposta:

x=10 m

Explicação passo-a-passo:

A área do retângulo (A)

A=x.(x+14)

Substituindo A=240

240=x.(x+14)

240=x²+14x

x²+14x-240=0

$\displaystyle Aplicando~a~f\acute{o}rmula~de~Bhaskara~para~x^{2}+14x-240=0~~e~comparando~com~(a)x^{2}+(b)x+(c)=0,~determinamos~os~coeficientes:~\\a=1{;}~b=14~e~c=-240\\\\C\acute{a}lculo~do~discriminante~(\Delta):&\\&~\Delta=(b)^{2}-4(a)(c)=(14)^{2}-4(1)(-240)=196-(-960)=1156\\\\C\acute{a}lculo~das~raizes:&\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(14)-\sqrt{1156}}{2(1)}=\frac{-14-34}{2}=\frac{-48}{2}=-24$$\displaystylex^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(14)+\sqrt{1156}}{2(1)}=\frac{-14+34}{2}=\frac{20}{2}=10$

Descartar x'=x= -24 porque não existe medida negativa

x''=x=10 m