Making a cube from prism

Question

We have a triangle base prism with lengths $1,2,\sqrt{5}$ (So it has right angle). The height of this prism is $1$. We want to cut it somehow such that by gluing two pieces, we can make a cube (equilateral cuboid). How this cut must be made?

For the solution, I know the cube volume will be 1 so the sides are $1,1,1$. But I don't know how this can be done?

Answer 1

Hint: in a rectangle $ABCD$ with $AB=1,BC=2$ let $E$ and $F$ be the midpoints of $BC$ and $AD$, respectively. Let the line $EF$ cross the diagonal $AC$ at $O$. Show the triangles $AFO$ and $CEO$ are equal.

Answer 2

After gluing together two given triangle prisms along their hypotenuse planes cut the newly formed cuboid measuring $(1,2,1)$ into two equal parts (bisecting sides of length $2)$ so that each half now becomes cube of size $(1,1,1)$

Length of each cube side unit $=1.$

Answer 3

Cut the triangle base into two parts that can be reassembled into a square.