Problem:
How many different isosceles triangles have integer side lengths and perimeter
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Because the perimeter of such a triangle is , and the sum of the two equal side lengths is even, the length of the base is odd. Also, the length of the base is less than the sum of the other two side lengths, so it is less than half of . Thus the six possible triangles have side lengths ; and .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions