Believe it or not - 5

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Dear All

There are only five Heronian triangles (triangles having integer sides) such that the perimeter is equal to the area. They are : (5, 12, 13) , (6, 8, 10) , (6, 25, 29) , (7, 15, 20) and
(9, 10, 17). The first two triangles are right triangles also.

Comments

  1. AnonymousJanuary 14, 2011 at 5:36 PM

    [a+b+c]squared = [s(s-a)(s-b)(s-c)]
    so,
    a2 + b2 + c2 + 2ab + 2bc + 2ca = [(a+b+c)(-a+b+c)(a-b+c)(a+b-c)]/ 16

    1) EQUILATERAL TRIANGLE
    => (3a4)/16 = (3a)2
    => a = root of 48 = 4 * root 3 = 4_|~3

    that is also a heronian triangle

    ReplyDelete

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