Problem: Let line AC be perpendicular to line CE. Connect A to D, the midpoint of CE and connect E to B, the midpoint of AC. If AD and EB intersect in point F, and BC=CD=15 inches, then the area of triangle DFE, in square inches, is:
Answer Choices:
A. 50
B. 502​
C. 75
D. 215​105​
E. 100
Solution:
Draw AE and the altitude FG to the base DE of triangle DEF. Since F is the intersection point of the medians of triangle ACE,FD=31​AD. ∴FG=31​AC=31​⋅30=10∴ area (△DEF)=21​⋅15⋅10=75
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