We can take
That is, x be the length and and the width of the rectangle. So we have the following system of linear equations:
[tex]\begin{gathered} \mleft\{\begin{aligned}x=6y\text{ (1)} \\ x+y+x+y=60\text{ (2)}\end{aligned}\mright. \\ \mleft\{\begin{aligned}x=6y\text{ (1)} \\ 2x+2y=60\text{ (2)}\end{aligned}\mright. \end{gathered}[/tex]Since to obtain the perimeter all the sides of the rectangle must be added.
[tex]\begin{gathered} 2(6y)+2y=60\text{ (2)} \\ 12y+2y=60 \\ 14y=60 \\ y=\frac{60}{14} \\ y=4.29 \end{gathered}[/tex]Now that we have the value of y we can plug it into equation (1)
[tex]\begin{gathered} x=6\cdot\frac{60}{14}\text{ (1)} \\ x=25.71 \end{gathered}[/tex]Finally, the dimensions of the rectangle are 25.7 cm long and 4.3 cm wide.
