Question 106679
To solve this question it is easier to make a set of simple equations.

because perimeter is x+y+z we can make the equation

{{{ab+bc+ac=26}}}
now we can make equations for the other parts of the question
because BC is {{{2/3}}} the length of Ab we can make the equation

{{{AB=(2/3)BC}}}

now we can add on the other part of the equation. because BC is 2cm longer than AC we can derive the equation

{{{AC=BC+2}}}

now you have the 3 equations below
{{{ab+bc+ac=26}}}
{{{AB=(2/3)BC}}}
{{{AC=BC+2}}}

the simplest way to solve is to substitute the 2 lower equations into the top equation in place of their respective variables. so you substitute (2/3)BC in place of AB in the top equation.

you get

{{{(2/3)BC+BC+BC+2=26}}}
simplify

{{{(8/3)BC=24}}}

divide by 8/3
BC=9
Now because you have BC solved substitute into the other equations to solve for the remainder sides
{{{AC=9+2}}}
{{{AB=(2/3)9}}}
so  AC=11
and AB=6

the lengths of the 3 sides of the triagle are 9,11,6