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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