Research suggests a T-Rex would need 50-100k kCal/day. Even if it ate a whole cow before starting, it would be hurting a week in.
Maybe it could survive the month, but would probably be severely malnourished at that point.
In any event, there is no mention of what happens if I fail to kill it. Does the experiment just end and I go home empty handed, or does the magic hut disappear and we fight it out to the death?

There are bad faith questions[1], (at least somewhat) self-answering questions[2], and poorly asked questions[3]. (Edit: this comm has rules. These and others are covered in the sidebar, It's not about being too stupid a question, it's about being appropriate for this community)
[1] "Are you still cheating on your spouse?" type questions that are meant to evoke a response rather than ask a real question that deserves an answer.
[2] is a little harder to define, but I have definitely seen a few where even the smallest amount of thought about what is being asked would make the answer obvious. (edit: I hope people aren't just drive-by downvoting this type, but I sort of understand why they might)
[3] includes questions that have so many answers depending on factors not specified that they're impossible to answer without writing a book covering every assumption that goes into each possibility.