the perimeter is the sum of the 3 sides of the triangle, hence
x + 1 + x + 2 + x + 2 = 32
3x + 5 = 32 ( subtract 5 from both sides )
3x = 27 ( divide both sides by 3 )
x = 9
EF = x + 1 = 9 + 1 = 10
FG = x + 2 = 9 + 2 = 11
EG = x + 2 = 9 + 2 = 11
check : 10 + 11 + 11 = 32 ← perimeter