Step 1: Recall the rule.
The perpendicular distance of a point \( (x, y) \) from the \(x\)-axis is \( |y| \).
Step 2: Substitute the coordinates.
For \( (13, 19) \), the distance from the \(x\)-axis is \( |19| = 19 \).
Step 3: Conclude.
Hence, the required length of the perpendicular is \( 19 \).