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Inside a square with side length 10, two congruent equilateral triangles are drawn such that they share one side and each has one vertex on a vertex of the square. What is the side length of the largest square that can be inscribed in the space inside the square and outside of the triangles?

 Feb 11, 2021
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Inside a square with a side length of 10, two congruent equilateral triangles are drawn such that they share one side and each has one vertex on a vertex of the square. What is the side length of the largest square that can be inscribed in the space inside the square and outside of the triangles?

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Triangle height: h = √50

 

Triangle side:  a = h / cos(30º)

 

Side of a small square: s = a * sin(15º)

 Feb 11, 2021

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