Question

el perimetro de un rectangulo mide 80 cm ¿cuanto mide su largo si su ancho es 3/4 del largo?

Answer 1

$Hola~~~\mathbb{TATIANA} \\ \\ Sea~la~figura:~~\boxed{\Bigg|~~~~~~~~~~~~~~\Bigg|}largo ~~\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ancho \\ \\ vamos~llamar: ~~\begin{cases} largo~---\ \textgreater \ y \\ \\ ancho~---\ \textgreater \ x\end{cases} \\ \\ Entonces~el~per\acute{i}metro~sera': \\ \\ 2y+2x=80cm~~~---\ \textgreater \ simplificando~nos~queda$

$\boxed{y+x=40cm }~------\ \textgreater \ (I) \\ \\ \\ Ahora~nos~dice~que: \\ \\ Su~ancho~es~3/4~del~largo, entonces~la~ecuaci\acute{o}n~seria: \\ \\ \boxed{x= \frac{3}{4}y}~--------\ \textgreater \ (II) \\ \\ \\ ====================================$
$Ahora~reemplazamos~(II)~en~(I)~vea: \\ \\ y+x=40cm~~--\ \textgreater \ tenemos~[ x= \frac{3}{4}y ~~] \\ \\ y+ \frac{3}{4}y =40cm \\ \\ \frac{4y+3y}{4}=40cm \\ \\ 7y=160cm \\ \\ y=22,85714....~~~~---\ \textgreater \ aproximando~seria \\ \\ \boxed{\boxed{y=22,86cm }}~----\ \textgreater \ valor~del~largo$

$===================================\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Espero~te~sirva~saludos!!$