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=302β242β=324β=18. (Or note that triangle AEB is similar to a 3β4β5 right triangle, so AE=3Γ6=18.)
Also CF=24 and FD=252β242β=49β=7. The perimeter of the trapezoid is 50+30+18+50+7+25=180.
Answer: Aβ.
The problems on this page are the property of the MAA's American Mathematics Competitions