If the length of the first piece is x then the others are of lengths 2x and 3x.
Furthermore,
[tex]42=x+2x+3x=6x[/tex]
Divide both ends by [tex]6[/tex] to find
[tex]x=7[/tex]
So the first piece is of length 7 inches and the other two are 14 inches and 21 inches.