Answer
The pieces are 54 cm and 42 cm long.
Work Step by Step
Let x be the length of the longer piece and y be the length of the shorter piece.
Together, the two pieces are 96 cm long, so:
$x+y=96$
The longer piece is 12 cm longer, so:
$x=y+12$
Substitute $y+12$ for $x$ in the first equation.
$y+12+y=96$ $\longrightarrow$ simplify
$2y+12=96$ $\longrightarrow$ subtract 12 from both sides
$2y+12-12=96-12$ $\longrightarrow$ simplify
$2y=84$ $\longrightarrow$ divide both sides by 2
$2y\div2=84\div2$ $\longrightarrow$ simplify
$y=42$
Substitute 42 for y in the second equation.
$x=42+12=54$
