The issue of weight (resistance) training in the gym and how "important" it is depends on many factors. The main ones being age, previous experience as a triathlete and also previous exposure to weights training. For most beginner triathletes, weights can be considered (somewhat) as an injury prevention measure. Resistance training, combined with an appropriate stretching or flexibility program, will help you strengthen muscles and connective tissue, which are often subject to overuse injuries in endurance athletes.
I would generally advise most beginning triathletes to follow a weights program during the off season, then focus their time and energy on swimming, cycling and running during the pre-season and race season. In the case of the inexperienced athlete, you will need to be "fresh" for your event-specific training, rather than fatigued from a weights session (the day before).
In some cases, a "Maintenance" phase of weights training would be appropriate during the race season. This would generally be for the experienced athlete and the older athlete - ie 40+
One should keep in mind, that there is an inbuilt "strength component" to most workouts. ie: pulling yourself through water, cycling against any resistance such as wind or a hill and running anywhere, takes some degree of STRENGTH.
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