Here we go !!
Since it's a regular pentagon, all it's sides are equal so let's solve for x
[tex] \hookrightarrow \: 3(x - 1) = 5x - 6[/tex]
[tex] \hookrightarrow \: 3x - 3 = 5x - 6[/tex]
[tex] \hookrightarrow \: 3x - 5x = - 6 + 3[/tex]
[tex] \hookrightarrow \: - 2x = - 3[/tex]
[tex] \hookrightarrow \: x = \dfrac{ - 3}{ - 2} [/tex]
[tex] \boxed{\boxed{x = \dfrac{3}{2} }}[/tex]
now let's find the measure of each side, i.e
[tex] \hookrightarrow \: 5x - 6[/tex]
[tex] \hookrightarrow \: (5 \times \dfrac{3}{2}) - 6[/tex]
[tex] \hookrightarrow \: \dfrac{15}{2} - 6[/tex]
[tex] \hookrightarrow \: 7.5 - 6[/tex]
[tex] \mathrm{\hookrightarrow \: 1.5 \: units}[/tex]
perimeter = 5 × side length ( for a regular pentagon )
[tex] \hookrightarrow \: 1.5 \times 5[/tex]
[tex] \boxed{ \boxed{ \: \: \: \: \: \: \: \: 7.5 \: \: units \: \: \: \: \: \: \: }}[/tex]
