Question

sabendo que a área da região retangular é 10cm², calcule o valor de x.


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Answer 1

$\boxed{\begin{array}{l}\sf A=c\cdot \ell\\\sf c\longrightarrow comprimento\\\sf \ell\longrightarrow largura\\\sf A=10~cm^2~~c=5\sqrt{2}~cm~~~\ell =x\\\sf A=c\cdot\ell\\\sf 10=5\sqrt{2}\cdot x\\\sf x=\dfrac{\diagdown\!\!\!\!\!\!10^2}{\diagdown\!\!\!5\sqrt{2}}\\\sf x=\dfrac{2}{\sqrt{2}}\\\underline{\rm racionalizando~temos\!:}\\\sf x=\dfrac{2}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}\\\sf x=\dfrac{2\sqrt{2}}{\sqrt{2^{\diagup\!\!\!\!2}}}\\\sf x=\dfrac{\backslash\!\!\!2\sqrt{2}}{\backslash\!\!\!2}\end{array}}$

$\Large\boxed{\begin{array}{l}\huge\boxed{\boxed{\boxed{\boxed{\sf x=\sqrt{2}~cm}}}}\end{array}}$