The Isosceles Right Triangle Puzzle

It is easy to completely cover an Isosceles Right Triangle with two congruent shapes without

any overlap. It is also easy is to do this with four congruent shapes. (see the diagram below)

Not so easy is how best to cover an Isosceles Right Triangle with three congruent shapes.

In fact, it is impossible to completely cover the triangle without overlap, but you can get close.

Your challenge: Find the shape that will best cover an Isosceles Right Triangle with

three congruent copies, and calculate what fraction of the triangle they can cover.