Problem:
Nondegenerate has integer side lengths, is an angle bisector, , and . What is the smallest possible value of the perimeter?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
By the Angle Bisector Theorem, . Thus must be a multiple of . If , the triangle is degenerate. If , then , and the perimeter is .
The problems on this page are the property of the MAA's American Mathematics Competitions