I have a question regarding the geometry question from this particular day. For the right triangle with a 12 perimeter, Greg assumed they were a 3,4,5 triplet and thus had an area of 6. However, they could be a 30-60-90 or 45-45-90 right triangle as well, right? The area would still be less than the equilateral triangle, but shouldn’t we have taken those cases into consideration?

If you know that regular polygon have the maximum area then no need to calculate anything otherwise you can test 1-2 other cases.

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