Take x and y as the sides if the rectangle
[tex]\begin{gathered} \frac{x}{y}=\frac{5}{3} \\ 3x=5y \end{gathered}[/tex][tex]2x+2y=32[/tex]Clear x from both equations
[tex]\begin{gathered} x=\frac{5}{3}y \\ x=\frac{32-2y}{2}=16-y \end{gathered}[/tex]Equal both expressions
[tex]\begin{gathered} \frac{5}{3}y=16-y \\ \frac{5}{3}y+y=16 \\ \frac{8}{3}y=16 \\ y=16\cdot\frac{3}{8} \\ y=6 \end{gathered}[/tex]Now find x using one of the first equations
[tex]\begin{gathered} x=16-y \\ x=16-6 \\ x=10 \end{gathered}[/tex]One of the sides measures 6cm and the other one 10cm
