Problem:
Square ABCD has side length 1. Points P,Q,R, and S each lie on a side of ABCD such that APQCRS is an equilateral convex hexagon with side length s. What is s?
Answer Choices:
A. 32
B. 21
C. 2−2
D. 1−42
E. 32
Solution:
Without loss of generality, assume that P and Q lie on AB and BC, respectively. Then AP=PQ=QC=s and PB=BQ=1−s, so PQ=2(1−s). Because APQCRS is equilateral, it follows that s=2(1−s), from which