Thread: 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"?

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:

               *
            *  |  *
         *     |     *
      *  *  *  *  *  *  *