Problem:
What is the perimeter of trapezoid ABCD?
Answer Choices:
A. 180
B. 188
C. 196
D. 200
E. 204
Solution:
By the Pythagorean Theorem, AE=302−242​=324​=18. (Or note that triangle AEB is similar to a 3−4−5 right triangle, so AE=3×6=18.)
Also CF=24 and FD=252−242​=49​=7. The perimeter of the trapezoid is 50+30+18+50+7+25=180.
Answer: A​.
The problems on this page are the property of the MAA's American Mathematics Competitions
