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### Best Answer CWanamaker says

Here is my solution.

The numbers in the interior of the triangle are: 3,8,10

The numbers on the vertices are: 4,5,12

3+8+10 = 4+5+12 = 21

3*8*10 = 4*5*12 = 240

The sides of the triangle are (4,7,11,13,5), (5,2,6,15,12), & (12,9,14,1,4) which all sum up to 40.

Very nice!

### paxwill says

I put 15, 14, and 3 in the middle and 7, 9, and 10 at the corners since 15*14*3 = 7*9*10 = 630, and since 15 + 14 + 3 = 32 and 7 + 9 + 10 = 26 have the same remainder mod 3. Then I determined that the sides had to add up to 38 since

(1+2+...+14+15) - (15+14+3) + (7+9+10) = 114

and 114/3 = 38. The side numbers are {7, 4, 6, 12, 9}, {9, 1, 5, 13, 10}, and {10, 2, 8, 11, 7}.