Question 969688
v, the vertex angle.
{{{v+x+x=180}}}
{{{v=180-2x}}}


One objective is to find a formula for the base length.
b, the length of the base.
Law of Cosines:
{{{3^2+3^3-2*3*3*cos(v)=b^2}}}


{{{18-18*cos(v)=b^2}}}
{{{b^2=18-18*cos(180-2x)}}}-----Think or inspect this angle on The Unit Circle.



....  {{{cos(180-2x)=-cos(2x)}}}.


Revise the equation for {{{b^2}}}.
{{{b^2=18+18*cos(2x)}}}


The isosceles triangle to have any meaning and match the given requirement,  {{{0<x<60}}}.


Perimeter:
{{{6+sqrt(18+18*cos(0))>perimeter>6+sqrt(18+18cos(120))}}}
{{{6+sqrt(18+18*1)>perimeter>6+sqrt(18+18*(-cos(60)))}}}, again refer to Unit Circle to see.
{{{6+sqrt(36)>perimeter>6+sqrt(18+18*(1/2))}}}
{{{12>perimeter>6+sqrt(27)}}}
{{{highlight(12>perimeter>6+3*sqrt(3))}}}