Start by sketching the situation, dividing the string into 3 pieces
Call the shortest piece as x
Then since the other pieces are a reference to the shortest side we can call them as:
[tex]\begin{gathered} x+2 \\ x+4 \end{gathered}[/tex]
Then, add them to the sketch
If we add together the 3 pieces they must be equal to the initial length of the string
[tex]x+(x+2)+(x+4)=108[/tex]
Simplify the left side of the equation
[tex]\begin{gathered} 3x+6=108 \\ \end{gathered}[/tex]
Solve the equation for x
[tex]\begin{gathered} 3x+6-6=108-6 \\ 3x=102 \\ x=\frac{102}{3} \\ x=34 \end{gathered}[/tex]
The shortest piece is 34 inches long.
The longest piece is 4 inches longer than the shortest, then,
[tex]34+4=38[/tex]
The longest piece is 38 inches long.
