Question

Qual o valor de x para a área do retângulo abaixo ser 30cm²
obs: Área: 30
base:x-2
altura: x-1​

Answer 1

$\boxed{\begin{array}{l}\sf(x-2)\cdot(x-1)=30\\\sf x^2-x-2x+2-30=0\\\sf x^2-3x-28=0\\\sf\Delta=b^2-4ac\\\sf\Delta=(-3)^2-4\cdot1\cdot(-28)\\\sf\Delta=9+112\\\sf\Delta=121\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\sf x=\dfrac{-(-3)\pm\sqrt{121}}{2\cdot1}\\\\\sf x=\dfrac{3\pm11}{2}\begin{cases}\sf x_1=\dfrac{3+11}{2}=\dfrac{14}{2}=7\\\\\sf x_2=\dfrac{3-11}{2}=-\dfrac{8}{2}=-4\end{cases}\\\\\sf como~x>0,a~resposta~\acute e~x=7\end{array}}$