By means of a tensor network algorithm, we have studied dimerized phases for a frustrated spin-l/2 ladder system.The ground-state fidelity per lattice, geometric entanglement, and string order parameters are computed.Our results are in sharp contrast with the previous results: we failed to detect a fragile columnar dimerized phase.In addition, a finite-entanglement scaling of the von Neumann entropy is performed with different bond dimensions, thus determining the central charge at a critical point.