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Mass, radius, and age are three of the most fundamental parameters for celestial objects, enabling studies of the evolution and internal physics of stars, brown dwarfs, and planets. Brown dwarfs are hydrogen-rich objects that are unable to sustain core fusion reactions but are supported from collapse by electron degeneracy pressure. As they age, brown dwarfs cool, reducing their radius and luminosity. Young exoplanets follow a similar behaviour. Brown dwarf evolutionary models are relied upon to infer the masses, radii and ages of these objects. Similar models are used to infer the mass and radius of directly imaged exoplanets. Unfortunately, only sparse empirical mass, radius and age measurements are currently available, and the models remain mostly unvalidated. Double-line eclipsing binaries provide the most direct route for the absolute determination of the masses and radii of stars. Here, we report the SPECULOOS discovery of 2M1510A, a nearby, eclipsing, double-line brown dwarf binary, with a widely-separated tertiary brown dwarf companion. We also find that the system is a member of the $45\pm5$ Myr-old moving group, Argus. The system's age matches those of currently known directly-imaged exoplanets. 2M1510A provides an opportunity to benchmark evolutionary models of brown dwarfs and young planets. We find that widely-used evolutionary models do reproduce the mass, radius and age of the binary components remarkably well, but overestimate the luminosity by up to 0.65 magnitudes, which could result in underestimated photometric masses for directly-imaged exoplanets and young field brown dwarfs by 20 to 35%.