Problem:
A paper triangle with sides of lengths , and inches, as shown, is folded so that point falls on point . What is the length in inches of the crease?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The paper's long edge is the hypotenuse of right triangle , and the crease lies along the perpendicular bisector of . Because , the crease hits rather than . Let be the midpoint of , and let be the intersection of and the line through perpendicular to . Then the crease in the paper
is . Because , it follows that . Thus
The problems on this page are the property of the MAA's American Mathematics Competitions