## Precalculus (6th Edition)

$x=6$ cm is the length of the shortest side.
The perimeter of a triangle can be calculated as: $P=a+b+c$, where a, b and c are the lengths of its sides Here: $a=2x$, $b=2x$, $c=x$, $P=30$ cm, by substituting, we get: $30=2x+2x+x$ $30=5x$ $x=6$ cm, this is the length of the shortest side.