Question 954953

{{{A=B-51}}}
.
.
{{{A+B+C=168}}}
{{{C=168-A-B}}}
{{{C=168-(B-51)-B}}}
{{{C=219-2B}}}
.
.
{{{A^2+B^2=C^2}}}
{{{(B-51)^2+B^2=(219-2B)^2}}}
{{{B^2-102B+2601+B^2=4B^2-876B+47961}}}
{{{2B^2-102B+2601=4B^2-876B+47961}}}
{{{2B^2-774B+45360=0}}}
{{{B^2-387B+22680=0}}}
{{{(B-315)(B-72)=0}}}
Only the solution that is less than 168 makes sense.
{{{B-72=0}}}
{{{B=72}}}
Then,
{{{A=72-51}}}
{{{highlight(A=21)}}}
and
{{{C=219-2(72)}}}
{{{C=219-144}}}
{{{C=75}}}