The layered perovskites RCr(BO3)2 (R = Y and Ho) with magnetic triangular lattices were studied by performing ac/dc susceptibility, specific heat, elastic and inelastic neutron scattering, and dielectric constant measurements. The results show (i) both samples' Cr 3+ spins order in a canted antiferromagnetic structure with TN around 8-9 K, while the Ho 3+ ions do not order down to T = 1.5 K in HoCr(BO3)2; (ii) when a critical magnetic field HC around 2-3 T is applied below TN , the Cr 3+ spins in the Y-compound and both the Cr 3+ and Ho 3+ spins in the Ho-compound order in a ferromagnetic state; (iii) both samples exhibit dielectric constant anomalies around the transition temperature and critical field, but the Ho-compound displays a much stronger magnetodielectric response. We speculate that this is due to the magnetostriction which depends on both of the Cr 3+ and the Ho 3+ ions' ordering in the Ho-compound. Moreover, by using linear spin wave theory to simulate the inelastic neutron scattering data, we estimated the Y-compound's intralayer and interlayer exchange strengths as ferromagnetic J1 = -0.12 meV and antiferromagnetic J2 = 0.014 meV, respectively. The competition between different kinds of superexchange interactions results in the ferromagnetic intralayer interaction.