  The Soft X-ray intensity of loops in active region cores and corresponding
footpoint, or moss, intensity observed in the EUV remain steady for several
hours of observation. The steadiness of the emission has prompted many to
suggest that the heating in these loops must also be steady, though no direct
comparison between the observed X-ray and EUV intensities and the steady
heating solutions of the hydrodynamic equations has yet been made. In this
paper, we perform these simulations and simultaneously model the X-Ray and EUV
moss intensities in one active regioncore with steady uniform heating. To
perform this task, we introduce a new technique to constrain the model
parameters using the measured EUV footpoint intensity to infer a heating rate.
We find that a filling factor of 8% and loops that expand with height provides
the best agreement with the intensity in two X-ray filters, though the
simulated SXT Al12 intensity is 147% the observed intensity and the SXT AlMg
intensity is 80% the observed intensity. From this solution, we determine the
required heating rate scales as ${\bar{B}}^{0.29} L^{-0.95}$. Finally we
discuss the future potential of this type of modeling, such as the ability to
use density measurements to fully constrain filling factor, and its
shortcomings, such as the requirement to use potential field extrapolations to
approximate the coronal field.
