If I want to know What's the minimal length of each side of an equilateral triangle that can get a square of which each of its sides is 15 mm, inside it (=inside the square)?. How to calculate it? (I'm not looking for the answer, but I'm looking for the way or approach to solving it, for future self-solutions).
2026-05-16 22:54:11.1778972051
What's the minimal length of each side of an equilateral triangle that can get a square of 15 mm inside it?
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Draw a pic. You'll want the square as big as possible, so it'll be tangent on a side and touching at two corners. Once you have the pic, think about what angles you know, and what the ratios between sides are in the known shapes (ex: squares have same sides, (30-60-90) triangles have $1-\sqrt 3-2$ sides).