Answer
The length of one piece is 12 feet.
The length of the other piece is 18 feet.
Work Step by Step
Let x represent the length of one piece.
The length of the other piece is 30 - x.
Now, let’s set up a proportion with the ratio given and a ratio which compares the corresponding lengths.
$\frac{2}{3}$ = $\frac{x}{(30-x)}$
To solve this equation, we equate the cross products.
2 $\times$ (30 - x) = x $\times$ 3
60 - 2x = 3x
60 = 5x
Divide both sides by 5.
x = 12
The length of one piece is 12 feet.
The length of the other piece is 30 - 12 = 18 feet.
