# Pythagorean isosceles triangle?

• Apr 3rd 2011, 10:21 PM
Wilmer
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"?
• Apr 4th 2011, 07:39 AM
Soroban
Helli, Wilmer!

Quote:

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:

```               *             *  |  *         *    |    *       *  *  *  *  *  *  *```