October 22, 2019

Problem of the Week

Tuesday, October 22, 2019

Triangle ABC is equilateral. It can be chopped up into four pieces that can be rearranged to make a square in the following way: D and E are midpoints of their corresponding sides, EF is constructed to be the length of the side of the square, G is found so that FG is equal in length to half the side of the triangle and H and I are found by drawing perpendicular lines to EF from G and D. If a triangular tabletop is constructed, the four pieces of which it is made can be attached by three hinges so that it can open up to form a square tabletop. Which of the points in this picture are where the hinges or rotation points are located?

Winners of triangle into square challenge