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 Integer Triangles (Posted on 2006-06-21)
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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 four more -- computer used | Comment 2 of 5 |
`6             8             105             12            139             10            177             15            206             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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