We report the discovery by the WASP transit survey of a giant planet in a close orbit (0.0295+-0.0009 AU) around a moderately bright (V=11.6, K=10) G9 dwarf (0.89+-0.08 M_sun, 0.84+-0.03 R_sun) in the Southern constellation Eridanus. Thanks to high-precision follow-up photometry and spectroscopy obtained by the telescopes TRAPPIST and Euler, the mass and size of this planet, WASP-50b, are well constrained to 1.47+-0.09 M_jup and 1.15+-0.05 R_jup, respectively. The transit ephemeris is 2455558.6120 (+-0.0002) + N x 1.955096 (+-0.000005) HJD_UTC. The size of the planet is consistent with basic models of irradiated giant planets. The chromospheric activity (log R'_HK = -4.67) and rotational period (P_rot = 16.3+-0.5 days) of the host star suggest an age of 0.8+-0.4 Gy that is discrepant with a stellar-evolution estimate based on the measured stellar parameters (rho_star = 1.48+-0.10 rho_sun, Teff = 5400+-100 K, Fe/H= -0.12+-0.08) which favours an age of 7+-3.5 Gy. This discrepancy could be explained by the tidal and magnetic influence of the planet on the star, in good agreement with the observations that stars hosting hot Jupiters tend to show faster rotation and magnetic activity (Pont 2009; Hartman 2010). We measure a stellar inclination of 84 (-31,+6) deg, disfavouring a high stellar obliquity. Thanks to its large irradiation and the relatively small size of its host star, WASP-50b is a good target for occultation spectrophotometry, making it able to constrain the relationship between hot Jupiters' atmospheric thermal profiles and the chromospheric activity of their host stars proposed by Knutson et al. (2010).