Problem:
The perimeter of an equilateral triangle exceeds the perimeter of a square by cm. The length of each side of the triangle exceeds the length of each side of the square by . The square has perimeter greater than . How many positive integers are not possible values for
Answer Choices:
A.
B.
C.
D.
E. infinitely many
Solution:
Let denote the length of each side of the triangle and denote the length of each side of the square, so that . Then , so that . Because is impossible. However, may take on any positive value, so all integral values of that exceed (as well as many non-integral values) are possible. Thus, only are excluded as integer values for .