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Math Help - Pythagorean isosceles triangle?

  1. #1
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    Pythagorean isosceles triangle?

    A pythagorean right triangle has integer sides and area. Everybody knows that!

    For each of these, 2 integer sided isosceles triangles with integer area exist:
    as example, 2 right triangles 3-4-5 can be used to make isosceles triangles 5-5-6 and 5-5-8.

    Is there any reasons why this is not "widely known/quoted"?
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  2. #2
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    Helli, Wilmer!

    A Pythagorean right triangle has integer sides and area. Everybody knows that!

    For each of these, two integer-sided isosceles triangles with integer area exist.
    Example: two 3-4-5 right triangles can be used to make isosceles triangles
    . . 5-5-6 and 5-5-8.

    Is there any reasons why this is not "widely known/quoted"?

    Maybe because it is "too obvious"?
    . . (Is there such a thing?)


    An integer-sided isosceles triangle (with an even base and integral altitude)
    . . can be bisected into two congruent Pythagorean triangles.

    Code:
    
              *
              |
             *|*
              |
            * | *
              |
           *  |  *
              |
          * * * * *


    These, in turn, can be assembled into another integer-sided isosceles triangle.

    Code:
    
                   *
                *  |  *
             *     |     *
          *  *  *  *  *  *  *
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