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 â–³EBA,â–³DBC, and â–³BFC 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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