Square Inscribed in an Isosceles Right Triangle
(Use the slider to enlarge/shrink the square.
The value of n gives the percent distance D has traveled
on the hypotenuse between M and N.)
One side of the square sits on the hypotenuse of the triangle,
and a third vertex is on the base of the triangle.
When the fourth vertex lands on the vertical side of the triangle,
then the square is said to be “inscribed in the triangle.”
- idea from George Polya

1- What is the area of the inscribed square?
2- Can you predict the area for different sized triangles?