SOLUTION: If the lengths of the sides of a triangle are integers and their product is 504, what is a possible perimeter of the triangle?

Question 147931: If the lengths of the sides of a triangle are integers and their product is 504, what is a possible perimeter of the triangle?
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
504 can be broken down into its prime divisors.

Then start breaking down the various 3-somes that can make up the product,504.
I count 19 possible perimeters shown after the 3-some.
(2, 2, 126)= 130
(2, 3, 84)= 89
(2, 4, 63)= 69
(2, 6, 42)= 50
(2, 7, 36)= 45
(2, 9, 28)= 39
(2, 12, 21)= 35
(2, 14, 18)= 34
(3, 3, 56)= 62
(3, 4, 42)= 49
(3, 6, 28)= 37
(3, 7, 24)= 34
(3, 8, 21)= 32
(3, 12, 14)= 29
(4, 6, 21)= 31
(4, 7, 18)= 29

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