Triangle Problem (Heron's Formula)?

Question

A triangle has the following properties:
1) It is scalene
2) It does not contain a right angle.
3) It has interger length sides
4) Its area is an integer.
Find the triangle with these properties which has the least perimeter.

[ Use Heron's Formula for the area of a triangle with sides a, b, c: where area = square root of s(s-a)(s-b)(s-c) where s is the semi perimeter (a+b+c)/2 ]

Answer 1

Zak is partly correct in that his site gives the solution. But his example has a right angle. I guess the first example is (4.13.15).

Answer 2

Heron s formula is a definite case of Brahmagupta s formula for the area of a cyclic quadrilateral; the two certainly one of that are particular circumstances of Bretschneider s formula for the area of a quadrilateral. In the two circumstances Heron s formula is gained by placing between the factors of the quadrilateral to 0. Heron s formula is likewise a definite case of the formula of the area of the trapezoid based in easy terms on its factors. Heron s formula is gained by placing the smaller parallel area to 0.

Answer 3

i dunno if this is correct, but just go through it just in case.
if perimeter is minimum and the triangle has integral sides, the perimeter can be 6 (1+2+3). so the semiperimeter comes out to be 3. and the area comes to zero which is an integer. but a triangle with zero area is absurd so??? just saying, in the previous answer, the person has suggested 6,8,10 which is a right angled triangle!!