Problem:
Rectangle ABCD has AB=8 and BC=6. Point M is the midpoint of diagonal AC, and E is on AB with ME⊥AC. What is the area of △AME?
Answer Choices:
A. 865
B. 325
C. 9
D. 875
E. 885
Solution:
By the Pythagorean Theorem, AC=10, so AM=5. Triangles AME and ABC are similar, so AMME=86 and ME=415. The area of △AME is 21⋅5⋅415=(D)875.
OR
As above, AM=5 and △AME and △ABC are similar with similarity ratio 5:8. Therefore
Area(△AME)=(85)2⋅Area(△ABC)=8252⋅28⋅6=(D)875
The problems on this page are the property of the MAA's American Mathematics Competitions
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