Problem:
The diagram shows an octagon consisting of 10 unit squares. The portion below PQ is a unit square and a triangle with base 5. If PQ bisects the area of the octagon, what is the ratio QYXQ.
Answer Choices:
A. 52
B. 21
C. 53
D. 32
E. 43
Solution:
The area below PQ is
1+21⋅5⋅(1+QY)25⋅(1+QY)1+QYQY=5=4=58=53
Then XQ=1−QY=1−53=52, so QYXQ=3/52/5=32.
Answer: D.
The problems on this page are the property of the MAA's American Mathematics Competitions
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