The perimeter of the given rectangle is:
[tex](2x+2\times30)\operatorname{cm}=2x\text{ cm+60 cm.}[/tex]
Since the perimeter must be equal to or smaller than 70 cm we can set the following inequality:
[tex]2x+60\leq70.[/tex]
Solving the above inequality for x, we get:
[tex]\begin{gathered} 2x\le70-60, \\ 2x\le10, \\ x\le\frac{10}{2}, \\ x\le5. \end{gathered}[/tex]
Answer: Recall that x must be greater than zero since it is the length of the side of the rectangle, then
[tex]0
