Question 161696
Calls the sides {{{S}}}
Call the base {{{B}}}
The perimeter is then {{{S + S + B}}}
{{{S + S + B = 84}}}
It is given that 
{{{B = (1/3)*S}}}, so
{{{S + S + (1/3)*S = 84}}}
Multiply both sides by {{{3}}}
{{{3*2*S + S = 252}}}
{{{7S = 252}}}
{{{S = 36}}}
{{{B = (1/3)*S}}}
{{{B = (1/3)*36}}}
{{{B = 12}}}cm
check:
{{{S + S + B = 84}}}
{{{36 + 36 + 12 = 84}}}
{{{84 = 84}}}
OK