One approach would be:
1. Delete the triangle
2. Extrude the edge to create a proper quad replacement.
3. Weld the vertices at the end as necessary.
Another approach would be:
1. Use the multi-cut tool to bisect the triangle (i.e., use the 90 degree corner to start your edge and finish the edge in the middle of the hypotenuse.
2. Move the vertex at the middle of the hypotenuse to your desired location (to create the rectangular shape).
3. Delete the edge you created without deleting the vertices.
