Question

El perímetro de un rectángulo es 128 cm. y la razón entre la medida de sus lados es
5 : 3. Calcula su área.

Answer 1

$Hola \\ \\ Un~rect\acute{a}ngulo~~~\boxed{~~~~~~~~~~~~\bigg|}~y \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x \\ \\ \underbrace{Per\acute{i}metro~(P)}_{128cm}=2x+2y \\ \\ 128=2x+2y \\ \\ \boxed{x=64-y}~~~----\ \textgreater \ (I) \\ \\ \mathbb{tttttttttttttttttttttttttttttttttttttt} \\ La~raz\acute{o}n~entre~sus~lados: \\ \frac{x}{y} = \frac{5}{3} \\ \\ \boxed{x= \frac{5y}{3}}~~----\ \textgreater \ (II) \\ \\ \mathbb{tttttttttttttttttttttttttttttttttttttt}$

$Igualemos~(I)=(II) \\ \\ 64-y= \frac{5y}{3} \\ \\ 192-3y=5y \\ \\ \boxed{\boxed{y=24cm}} \\ \\ de~(I)~~x=64-y~~~--\ \textgreater \ calculemos~(x) \\ \\ ~~~~~~~~~~x=64-24 \\ \\ ~~~~~~~~~~\boxed{\boxed{x=40cm}} \\ \\ \mathbb{ttttttttttttttttttttttttttttttttttttttt} \\ Como~nos~pide~~\boxed{\acute{a}rea~(A)=x.y} \\ \\ A=40.(24) \\ \\ \boxed{\boxed{A=960cm\²}}~--\ \textgreater \ respuesta$

$\mathbb{iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii} \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Saludos!!$