The width of the garden is \(\frac{x}{3}-5\) (dm)
Because area of this garden is 252, we have:
\(x\left(\frac{x}{3}-5\right)=252\)
\(\Leftrightarrow\frac{1}{3}x^2-5x-252=0\Rightarrow x=36\) (dm)
\(\Rightarrow\) The width of the garden: \(\frac{36}{3}-5=7\) (dm)
\(\Rightarrow\) The perimeter: \(\left(36+7\right).2=84\) (dm)