Dudeney Dissection An equilateral triangle and interior is dissected according to the spec...

Dudeney Dissection An equilateral triangle and interior is dissected according to the specifications shown. Make a paper or cardboard model, using a carefully constructed figure, and having the exact dimensions specified.

AP = PB = AQ = QC = 5 cm

RS = 5 cm (BR > SC)

Find a way to reassemble these four pieces to form a square, and try to prove the validity of this dissection. (Hint: Think of quadrilateral BPXR and triangle CQR as pivoting about points P and Q, respectively, and triangle RYS about S.) NOTE: This construction is due to H. E. Dudeney (1857-1931) who discovered many ingenious dissections, some of which are considered here.