The shorter piece is $12$ inches long whereas the longer piece is $24$ inches long.
Work Step by Step
To solve this problem, you need to translate the problem into an algebraic expression. Let us set the shorter piece as $x$. The longer piece we can set in terms of $x$. We know that the longer piece is twice as long as the shorter one, so this piece can be represented as: longer piece $ = 2x$ We know that these two pieces added together should equal $36$ inches, so we can now put the pieces together and set up the equation: $$36 = 2x + x$$ We combine like terms: $$3x = 36$$ We solve for $x$ by dividing by $3$ on each side: $$x = 12$$ The shorter piece is $12$ inches long. To find the length of the longer piece, we plug in $12$ for $x$ for the expression we figured out to find the value of the longer piece: longer piece $ = 2(12)$ The longer piece is 24 inches long.