The perimeter of the given rectangle is:
![(2x+2*30)\operatorname{cm}=2x\text{ cm+60 cm.}]()
Since the perimeter must be equal to or smaller than 70 cm we can set the following inequality:
![2x+60\leq70.](https://img.qammunity.org/2023/formulas/mathematics/college/qhdloeugps1umj0yag710u8xjgl0jyree9.png)
Solving the above inequality for x, we get:
![\begin{gathered} 2x\le70-60, \\ 2x\le10, \\ x\le(10)/(2), \\ x\le5. \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/30qjoogyidnffj57cwcjz3394nq2h22xt7.png)
Answer: Recall that x must be greater than zero since it is the length of the side of the rectangle, then
[tex]0