Solution:
Let \(x\) be the first part and \(y\) be the second part.
\(x + y = 20\)
The ratio is 3:7, thus \(3:7 = x:y\)
\(\frac{3}{7} = \frac{x}{y}\)
\(x = \frac{3y}{7}\)
\(\frac{3y}{7} + y = 20\)
\(\frac{10y}{7}=20\)
\(y = 14\)
\(x = 20-14 = 6\)
Thus, the length of the shorter part is 6 inches and the longer part is 14 inches.