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Integer Triangles (Posted on 2006-06-21) Difficulty: 3 of 5
Find all integer sided triangles whose area and perimeter have the same numerical value.

See The Solution Submitted by Bractals    
Rating: 4.0000 (1 votes)

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Solution four more -- computer used | Comment 2 of 5 |
6             8             10
5             12            13
9             10            17
7             15            20
6             25            29

There might be some larger triangles, extremely thin, but it looks as if they stop here.

List produced by

DEFDBL A-Z
FOR t = 3 TO 1000000
  FOR a = 1 TO t / 3
  FOR b = a TO (t - a) / 2
  IF b > t / 2 - a THEN
    c = t - a - b: s = t / 2
    areasq = s * (s - a) * (s - b) * (s - c)
    area = INT(SQR(areasq) + .5)
    IF area * area = areasq THEN
      IF area = t THEN
        PRINT a, b, c
      END IF
    END IF
  END IF
  NEXT b
  NEXT a
NEXT t


  Posted by Charlie on 2006-06-21 16:08:16
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