Problem: The sides of a triangle are integers, and its area is also an integer. One side is and the perimeter is . The shortest side is:
Answer Choices:
A.
B.
C.
D.
E.
Solution:
. Simplifying, we obtain . . The smallest integer y that makes x an integer is , and, for this value, . For , so that . For larger values of , we obtain impossible triangles.
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