SOLUTION: The length of each side of a scalene triangle ABC is a prime number. Find the smallest possible perimeter

Question 438105: The length of each side of a scalene triangle ABC is a prime number. Find the smallest possible perimeter
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Note that a triangle with sides 2, x, and x+2 is impossible, since 2 + x = x+2, which violates the triangle inequality. Also, if x+2 is replaced with a larger number, this would still be impossible. Thus, the smallest side of the triangle must be at least 3.

Guessing and checking, we see that a triangle with sides 3, 5, 7 satisfies, and the perimeter is 15.
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