The perimeter is the sum of all sides.
The perimeter of the regular pentagon is five times its given expression because it has 5 equal sides.
[tex]P_{penta}=5(2x+9)[/tex]If the square has a side length of 3x, then its perimeter is
[tex]P_{square}=4(3x)[/tex]Since both figures have the same perimeter, we express the following equation.
[tex]\begin{gathered} P_{penta}=P_{square} \\ 5(2x+9)=4(3x) \end{gathered}[/tex]Now, we solve for x.
[tex]\begin{gathered} 10x+45=12x \\ 45=12x-10x \\ 2x=45 \\ x=\frac{45}{2} \\ x=22.5 \end{gathered}[/tex]