Question 389316
Let the three sides be: {{{x}}}, {{{(x+2)}}}, {{{(x+4)}}}
then the perimeter:
{{{p = x + (x+2) + (x+4)}}}
{{{p = 3x + 6}}}

- the longest side is it is {{{22}}} units shorter than the perimeter, so you will have

{{{(3x+6) - (x+4) = 22}}}

{{{3x + 6 - x - 4 = 22}}}

{{{2x + 2 = 22}}}

{{{2x = 22 - 2}}}

{{{2x = 20}}}

{{{x = 10}}}, ........the shortest side
then

{{{10 + 4 = 14}}} units is the longest side


Check solution
{{{Perimeter - longest side = (10+12+14) - 14 = 22}}}