Question

Um retângulo tem área 4w² - 144. Quais os polinômios que representam os lados desse retângulo

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm Fatorac_{\!\!,}\tilde ao~da~diferenc_{\!\!,}a}\\\underline{\rm de~dois~quadrados}\\\\\huge\boxed{\boxed{\boxed{\boxed{\sf a^2-b^2=(a-b)\cdot(a+b)}}}}\\\underline{\rm \acute Area~do~ret\hat angulo~de~dimens\tilde oes~c~e~\ell}\\\\\huge\boxed{\boxed{\boxed{\boxed{\sf A=c\cdot \ell}}}}\\\sf c\longrightarrow comprimento\\\sf \ell\longrightarrow largura\end{array}}$

$\Large\boxed{\begin{array}{l}\tt dados\begin{cases}\sf A=4w^2-144\\\sf c=?\\\sf \ell=?\end{array}\\\underline{\rm soluc_{\!\!,}\tilde ao:}\\\sf 4w^2-144=(2w-12)\cdot(2w+12)\\\sf A=c\cdot \ell\\\sf c\cdot \ell=4w^2-144\\\sf c\cdot \ell=(2w-12)\cdot(2w+12)\\\sf\iff c=2w-12~e~\ell=2w+12\end{array}}$