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Question 234489: The length of each side of triangle ABC is a prime number. Its
perimeter is also a prime number. Find the smallest possible perimeter.
Found 2 solutions by checkley77, MathTherapy:
Answer by checkley77(12844)   (Show Source):
Answer by MathTherapy(10555)  (Show Source):
You can put this solution on YOUR website! The length of each side of triangle ABC is a prime number. Its
perimeter is also a prime number. Find the smallest possible perimeter.
Since a prime number is any integer greater than 1, and the smallest prime number is 2, neither a side of the triangle nor its perimeter will be less than 2.
If we include 2 as a side of the triangle, we will not get a prime number but an even number instead, as, 2 odds added to an even will give us an even, which would give us a composite number.
Therefore, only 3 odd prime integers will add up to a prime number.
Now, let's list a few lower prime numbers, excluding 2. These are: 3, 5, 7, 11, 13
It obviously looks like we can use 3, 3, and 5, as these add up to 11, another
prime number.
Therefore, our side values are  , which makes the smallest possible prime perimeter:  (3 + 3 + 5)
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