Problem:
Rectangle ABCD has AB=4 and BC=3. Segment EF is constructed through B so that EF⊥DB, and A and C lie on DE and DF, respectively. What is EF?
Answer Choices:
A. 9
B. 10
C. 12125
D. 9103
E. 12
Solution:
Note that DB=5 and △EBA,△DBC, and △BFC are all similar.
Therefore EB4=53, so EB=320. Similarly, BF3=54, so BF=415.
Thus
EF=EB+BF=320+415=(C)12125
The problems on this page are the property of the MAA's American Mathematics Competitions
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