The relationship between the characteristic radii and masses (luminosities) of rich clusters of galaxies is studied using N-body simulations in comparison with observations. Various scenarios for the formation of the large-scale structure of the universe within the gravitational instability picture are considered, including hierarchical clustering, pancake, and hybrid scenarios. A well-defined radius-mass relation is found for the simulated clusters in each model, the slope of which depends on the form of the initial density fluctuation spectrum. The radius-luminosity relation is also studied for a sample of 29 Abell clusters, and a well-defined correlation is found to exist, R is proportional to L^0.51 +/= 0.07^. If M/L is roughly the same among clusters, and if the distributions of light and mass are similar, then best agreement with the observations is found for an initial spectrum with an effective slope -1 <= n <= 0 on the scale of protoclusters, as is expected in such scenarios as cold dark matter, isocurvature baryonic models, and certain hybrid scenarios. The pancake scenario, on the other hand, may have difficulty reproducing the observed radius-luminosity relation.