Problem:
In the figure, ABCD is a rectangle and EFGH is a parallelogram. Using the measurements given in the figure, what is the length d of the segment that is perpendicular to HE and FG?
Answer Choices:
A. 6.8
B. 7.1
C. 7.6
D. 7.8
E. 8.1
Solution:
By the Pythagorean Theorem, HE=5. Rectangle ABCD has area 10×8=80, and the corner triangles have areas 21​×3×4=6 and 21​×6×5=15. So the area of EFGH is 80−(2)(6)−(2)(15)=38. Because the area of EFGH is EH×d and EH=5,38=5×d, so d=7.6.
Answer: C​.
The problems on this page are the property of the MAA's American Mathematics Competitions
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