Question 220428
First, lets write all the lengths in terms of side A, since the relations all go back to it.
So, Side C:
{{{A=C+1}}}
{{{A-1=C}}}
Side B:
{{{2A=B}}}
Side A:
{{{A=A}}}
So, we knew that {{{A+B+C=51}}}. However, know we have what C and B are, so we can rewrite:
{{{A+2A+A-1=51}}}
Move the 1 to the other side and combine the {{{A}}} terms:
{{{4A=52}}}
Divide both sides by 4
{{{A=13}}}.
Substituting back in for C & B give us:
{{{B=26}}}, {{{C=12}}}.
The longest side is then {{{B=26}}}.