This study explores the steady-state propagation of hydraulic fractures in ductile and elastic media, with an emphasis on time-varying fracture geometry. A series of well-controlled experiments was performed, in which the hydraulic fracture propagation behaviors in two-dimensionally confined gelatin plates were monitored while varying the gelatin stiffness, fracturing fluid viscosity, and injection flow rate. In all cases, comet-shaped, bi-wing fractures were initiated, and the fluid pressure responses and fracture geometry, including propagation velocity, length, width, and opening area were analyzed using the acquired time-lapsed images. The fracture propagation initiated before the peak pressure value, and the initiation pressure increased with the gelatin stiffness, injection flow rate, and viscosity, however, mainly governed by the elastic stiffness. Contrary to theoretical models, two states were identified over the course of comet-shaped hydraulic fracture propagation: a transient state in which the fracture propagation velocity and fracture width gradually increased, and thereafter, a steady state where the velocity and width became consistent. As a result, the steady-state propagation velocity was primarily determined by the flow rate, and the fracture width in a steady state was proportional to the fluid pressure normalized by the medium stiffness, owing to the elastic response. Based on experimental observations, simple but robust semi-empirical models were suggested to predict the fracture width and propagation velocity in a steady state.