This is follow-on from Minimum area of Inscribed Square
If I have square S with perimeter 40, i.e. each side 10, and I have inscribed square T, what is the Maximum area of T?
How do I even go about solving this?
2026-02-25 00:28:21.1771979301
Maximum area of inscribed square
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If a square is inscribed in this larger square, all of its vertices must lie on the vertices of the larger square. This problem is trivial - just make the squares the same size by placing the vertices of the inscribed square atop the vertices of the original square. The answer is $10^{2} = \boxed{100}.$