Square in a Triangle - II

... adapted from Polya The challenge is inscribe a square in a triangle - two vertices of the square should lie on the base of the triangle. You can vary the triangle by dragging the WHITE dots. You can vary the inscribed rectangle by dragging the YELLOW dot. Can it always be done? Can you inscribe a cube in a tetrahedron - with one face of the cube lying on base of the tetrahedron ? What other questions [could,would] you ask of your students?