+214 Inside a square with side length , 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?
+1347 Let O be the center of the square, and let E, F, G, and H be the points where the sides of the square intersect the sides of the triangles. Since the triangles are equilateral, OE=OF=OG=OH=5. Let s be the side length of the largest square that can be inscribed in the space inside the square and outside of the triangles. Since O is the center of the square, s must be less than 5.
Let x=OE−s. Since s is the side length of the inscribed square, OE+s=OE−x+2s=OE+x=5. Therefore, x=2.
Since OE=5, the side length of the inscribed square is s=OE−2=5−2=3.
