Problem:
Three one-inch squares are placed with their bases on a line. The center square is lifted out and rotated , as shown. Then it is centered and lowered into its original location until it touches both of the adjoining squares. How many inches is the point from the line on which the bases of the original squares were placed?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Consider the rotated middle square shown in the figure. It will drop until length is inch. Thus
Hence . This is added to the inch height of the supporting squares, so the overall height of point above the line is
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions